WebDAV File System provides you an ability to access to your WebDAV storage directly from the Files app.
Go to WebDAV File System page on Chrome WebStore
$ git clone https://github.com/yoichiro/chromeos-filesystem-webdav.git
$ cd chromeos-filesystem-webdav
$ npm install
$ grunt
All files are licensed under the BSD license. See the LICENSE file for details. All original source code is Copyright 2015 Yoichiro Tanaka.