ClickOnce and Google Chrome don’t pal up each other. If ClickOnce application is configured to be installed from a server and when you click on its link in Google Chrome then the browser will download the file and you will try to install the app from your local path. But a reference to its manifest file will be relative to this local path when the manifest itself will be located at the server. Of course, IE services the *.application links correctly. And yeah, the related error would be in the details like this:
Downloading file:///*.exe.manifest did not succeed
P.S.: To fix that for Chrome one could download from Google Webstore an extension called “ClickOnce for Google Chrome™” which handles those links as desired.