Apps, Extensions and scripts cannot be added from this website

Instead of opening the file, you have to: extract it (crx are zip files), then visit chrome://extensions, enable developer mode, and load unpacked extension.

The reason for this is: lots of people try to abuse chrome apps/extensions to install nasty applications to your browser. So Chrome tries to make it impossible to automatically side-load these apps without you making sure that is really what you want to do.

So.. typical caveats of installing software apply when using this approach.

You can now also just drag-and-drop the .crx file onto the chrome://extensions page and it will install, too.

Edit 2019-01-10: Make sure to enable Developer mode for extensions. If this was not enabled, refresh the chrome://extensions page after enabling it.

Edit 2018-08-24: This works on Windows, too.

Edit:This doesn't work on Windows. Verified on OSX and ChromeOS. From what I've read, this will work on Linux, too.~

(I initially experienced the same problem you described.*)This solution worked for me in Windows 10 (build th1511) x64:

1. Open Chrome as you normally would.
2. Go to the "Extensions" page (chrome://extensions; or click Menu button at top right corner → From 'More tools' drop down menu select 'Extensions').
3. Drag and drop the .crx file onto the extensions page in Chrome -onto the list of extensions.You should see a dialog stating "Drop here to install". This must be present. (If you do NOT see this, reposition your mouse - it may be too far to the side of the page.)

It should load successfully and you should see the extension in the list immediately afterward.

*I received the same error you described when attempting to load the .crx file (packed extension) by right-clicking/double-clicking it and selecting "Open With" "Chrome", and by dragging/dropping the file onto a regular webpage in Chrome.