Google Chrome extension for Click Once?
Google Chrome doesn't really support extensions adding the .NET version to the user agent but for plain launching .applications give this a try:
https://chrome.google.com/extensions/detail/eeifaoomkminpbeebjdmdojbhmagnncl (No more available)
Chrome is not capable of auto-launching the setup.exe like Explorer does, but Chrome does download it like any other file. It's not difficult for the user to run it once it is downloaded until Chrome comes up with a way to cause it to automatically launch.
Install IETab for Chrome, then set up the rules to always open the launching page with IETab.