diff --git a/DESCRIPTION b/DESCRIPTION
index 5be2bb529..4e44760c6 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -64,6 +64,7 @@ Collate:
     'equals_na_linter.R'
     'exclude.R'
     'expect_lint.R'
+    'expect_not_linter.R'
     'expect_null_linter.R'
     'expect_type_linter.R'
     'extract.R'
diff --git a/NAMESPACE b/NAMESPACE
index fe9d2a911..d563fed50 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -31,6 +31,7 @@ export(duplicate_argument_linter)
 export(equals_na_linter)
 export(expect_lint)
 export(expect_lint_free)
+export(expect_not_linter)
 export(expect_null_linter)
 export(expect_type_linter)
 export(extraction_operator_linter)
diff --git a/NEWS.md b/NEWS.md
index 0cd733698..64ae49a9f 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -89,6 +89,7 @@ function calls. (#850, #851, @renkun-ken)
 * `lintr` is adopting a new set of linters provided as part of Google's extension to the tidyverse style guide (#884, @michaelchirico)
    + `expect_null_linter()` Require usage of `expect_null(x)` over `expect_equal(x, NULL)` and similar
    + `expect_type_linter()` Require usage of `expect_type(x, t)` over `expect_equal(typeof(x), t)` and similar
+   + `expect_not_linter()` Require usage of `expect_false(x)` over `expect_true(!x)`, and _vice versa_.
 * `assignment_linter()` now lints right assignment (`->` and `->>`) and gains two arguments. `allow_cascading_assign` (`TRUE` by default) toggles whether to lint `<<-` and `->>`; `allow_right_assign` toggles whether to lint `->` and `->>` (#915, @michaelchirico)
 
 # lintr 2.0.1
diff --git a/R/expect_not_linter.R b/R/expect_not_linter.R
new file mode 100644
index 000000000..c7e3d85d3
--- /dev/null
+++ b/R/expect_not_linter.R
@@ -0,0 +1,35 @@
+#' Require usage of expect_false(.) over expect_true(!.)
+#'
+#' [testthat::expect_false()] exists specifically for testing that an output is
+#'   `FALSE`. [testthat::expect_true()] can also be used for such tests by
+#'   negating the output, but it is better to use the tailored function instead.
+#'   The reverse is also true -- use `expect_false(A)` instead of
+#'   `expect_true(!A)`.
+#'
+#' @evalRd rd_tags("expect_not_linter")
+#' @seealso [linters] for a complete list of linters available in lintr.
+#' @export
+expect_not_linter <- function() {
+  Linter(function(source_file) {
+    if (length(source_file$parsed_content) == 0L) {
+      return(list())
+    }
+
+    xml <- source_file$xml_parsed_content
+
+    xpath <- "//expr[
+      SYMBOL_FUNCTION_CALL[text() = 'expect_true' or text() = 'expect_false']
+      and following-sibling::expr[1][OP-EXCLAMATION]
+    ]"
+
+    bad_expr <- xml2::xml_find_all(xml, xpath)
+
+    return(lapply(
+      bad_expr,
+      xml_nodes_to_lint,
+      source_file = source_file,
+      message = "expect_false(x) is better than expect_true(!x), and vice versa.",
+      type = "warning"
+    ))
+  })
+}
diff --git a/inst/lintr/linters.csv b/inst/lintr/linters.csv
index be4751581..ce0dcbf02 100644
--- a/inst/lintr/linters.csv
+++ b/inst/lintr/linters.csv
@@ -9,6 +9,7 @@ commented_code_linter,style readability best_practices default
 cyclocomp_linter,style readability best_practices default configurable
 duplicate_argument_linter,correctness common_mistakes configurable
 equals_na_linter,robustness correctness common_mistakes default
+expect_not_linter,package_development best_practices readability
 expect_null_linter,package_development best_practices
 expect_type_linter,package_development best_practices
 extraction_operator_linter,style best_practices
diff --git a/man/best_practices_linters.Rd b/man/best_practices_linters.Rd
index 38b823abb..b84a09504 100644
--- a/man/best_practices_linters.Rd
+++ b/man/best_practices_linters.Rd
@@ -15,6 +15,7 @@ The following linters are tagged with 'best_practices':
 \item{\code{\link{absolute_path_linter}}}
 \item{\code{\link{commented_code_linter}}}
 \item{\code{\link{cyclocomp_linter}}}
+\item{\code{\link{expect_not_linter}}}
 \item{\code{\link{expect_null_linter}}}
 \item{\code{\link{expect_type_linter}}}
 \item{\code{\link{extraction_operator_linter}}}
diff --git a/man/expect_not_linter.Rd b/man/expect_not_linter.Rd
new file mode 100644
index 000000000..cb11b7baf
--- /dev/null
+++ b/man/expect_not_linter.Rd
@@ -0,0 +1,19 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/expect_not_linter.R
+\name{expect_not_linter}
+\alias{expect_not_linter}
+\title{Require usage of expect_false(.) over expect_true(!.)}
+\usage{
+expect_not_linter()
+}
+\description{
+\code{\link[testthat:logical-expectations]{testthat::expect_false()}} exists specifically for testing an output is
+\code{FALSE}. \code{\link[testthat:logical-expectations]{testthat::expect_true()}} can also be used for such tests by
+negating the output, but it is better to use the tailored function instead.
+}
+\seealso{
+\link{linters} for a complete list of linters available in lintr.
+}
+\section{Tags}{
+\link[=best_practices_linters]{best_practices}, \link[=package_development_linters]{package_development}, \link[=readability_linters]{readability}
+}
diff --git a/man/linters.Rd b/man/linters.Rd
index d36397bff..6c3353f97 100644
--- a/man/linters.Rd
+++ b/man/linters.Rd
@@ -17,15 +17,15 @@ Documentation for linters is structured into tags to allow for easier discovery.
 \section{Tags}{
 The following tags exist:
 \itemize{
-\item{\link[=best_practices_linters]{best_practices} (12 linters)}
+\item{\link[=best_practices_linters]{best_practices} (13 linters)}
 \item{\link[=common_mistakes_linters]{common_mistakes} (5 linters)}
 \item{\link[=configurable_linters]{configurable} (16 linters)}
 \item{\link[=consistency_linters]{consistency} (7 linters)}
 \item{\link[=correctness_linters]{correctness} (7 linters)}
 \item{\link[=default_linters]{default} (25 linters)}
 \item{\link[=efficiency_linters]{efficiency} (4 linters)}
-\item{\link[=package_development_linters]{package_development} (4 linters)}
-\item{\link[=readability_linters]{readability} (21 linters)}
+\item{\link[=package_development_linters]{package_development} (5 linters)}
+\item{\link[=readability_linters]{readability} (22 linters)}
 \item{\link[=robustness_linters]{robustness} (10 linters)}
 \item{\link[=style_linters]{style} (32 linters)}
 }
@@ -43,6 +43,7 @@ The following linters exist:
 \item{\code{\link{cyclocomp_linter}} (tags: best_practices, configurable, default, readability, style)}
 \item{\code{\link{duplicate_argument_linter}} (tags: common_mistakes, configurable, correctness)}
 \item{\code{\link{equals_na_linter}} (tags: common_mistakes, correctness, default, robustness)}
+\item{\code{\link{expect_not_linter}} (tags: best_practices, package_development, readability)}
 \item{\code{\link{expect_null_linter}} (tags: best_practices, package_development)}
 \item{\code{\link{expect_type_linter}} (tags: best_practices, package_development)}
 \item{\code{\link{extraction_operator_linter}} (tags: best_practices, style)}
diff --git a/man/package_development_linters.Rd b/man/package_development_linters.Rd
index 2ced927e3..6fbc2e23b 100644
--- a/man/package_development_linters.Rd
+++ b/man/package_development_linters.Rd
@@ -13,6 +13,7 @@ Linters useful to package developers, for example for writing consistent tests.
 The following linters are tagged with 'package_development':
 \itemize{
 \item{\code{\link{backport_linter}}}
+\item{\code{\link{expect_not_linter}}}
 \item{\code{\link{expect_null_linter}}}
 \item{\code{\link{expect_type_linter}}}
 \item{\code{\link{package_hooks_linter}}}
diff --git a/man/readability_linters.Rd b/man/readability_linters.Rd
index 4e9be19c7..6795161e1 100644
--- a/man/readability_linters.Rd
+++ b/man/readability_linters.Rd
@@ -17,6 +17,7 @@ The following linters are tagged with 'readability':
 \item{\code{\link{commas_linter}}}
 \item{\code{\link{commented_code_linter}}}
 \item{\code{\link{cyclocomp_linter}}}
+\item{\code{\link{expect_not_linter}}}
 \item{\code{\link{function_left_parentheses_linter}}}
 \item{\code{\link{infix_spaces_linter}}}
 \item{\code{\link{line_length_linter}}}
diff --git a/tests/testthat/test-expect_not_linter.R b/tests/testthat/test-expect_not_linter.R
new file mode 100644
index 000000000..7f7defe14
--- /dev/null
+++ b/tests/testthat/test-expect_not_linter.R
@@ -0,0 +1,37 @@
+test_that("expect_not_linter skips allowed usages", {
+  expect_lint("expect_true(x)", NULL, expect_not_linter())
+  # NB: also applies to tinytest, but it's sufficient to test testthat
+  expect_lint("testthat::expect_true(x)", NULL, expect_not_linter())
+  expect_lint("expect_false(x)", NULL, expect_not_linter())
+  expect_lint("testthat::expect_false(x)", NULL, expect_not_linter())
+
+  # not a strict ban on !
+  ##  (expect_false(x && y) is the same, but it's not clear which to prefer)
+  expect_lint("expect_true(!x || !y)", NULL, expect_not_linter())
+})
+
+test_that("expect_not_linter blocks simple disallowed usages", {
+  expect_lint(
+    "expect_true(!x)",
+    "expect_false\\(x\\) is better than expect_true\\(!x\\)",
+    expect_not_linter()
+  )
+
+  expect_lint(
+    "testthat::expect_true(!x)",
+    "expect_false\\(x\\) is better than expect_true\\(!x\\)",
+    expect_not_linter()
+  )
+
+  expect_lint(
+    "expect_false(!foo(x))",
+    "expect_false\\(x\\) is better than expect_true\\(!x\\)",
+    expect_not_linter()
+  )
+
+  expect_lint(
+    "testthat::expect_true(!(x && y))",
+    "expect_false\\(x\\) is better than expect_true\\(!x\\)",
+    expect_not_linter()
+  )
+})