Chrome likes to hold onto old favicons. Hard refreshing, clearing dns, etc don't seem to do anything to update them. However, there is a fairly simple way to force a refresh.
All you have to do is type the favicon's url into the browser `www.website.com/images/favicon.ico' and have the browser load it (ctrl+f5). It will then automatically download the favicon, which you can delete if you want. Finally, without changing url locations, execute a refresh and the favicon should update for you.