google chrome get's a "Do you really want to start" prompt, but it's installed
Try executing from the Terminal the following command:

sudo xattr -d com.apple.quarantine /Applications/Google\ Chrome.app/


(it might ask you for your password, that's ok)

This basically clears the quarantine flag in the metadata for the file (this is not a flag in the file itself so it doesn't get carried away when you move or copy the file to another machine)