I have tried to do the Chrome on a different partition and just found it was easiest to install it, and then use mklink to make it a symbolic link on another partition. The only reason I installed it on another partition was because I was testing it from a RAM drive to see it's performance. (wasn't worth it vs my SSD)
You can also redirect user profile folders by adding a flag to the Chrome shortcut you use...
For isntance: "C:\Program Files (x86)\Google\Chrome\Application\chrome.exe" --user-data-dir="x:\Chrome"
But I found this cumbersome as it does not use that user data folder if you click a hyperlink (theoretically you could hop in the registry and change all of Chrome's launch point's to use the parameter.. but my god).