A screenshot might have helped, but then again probably not if all it shows is a chrome logo on the desktop.
But how do you know it was Avast that did this (I guess this is the kind of detail Asyn was talking about) ?
There are other programs, etc. that offer and or install Chrome.
I have been using Avast Free for over 16 years long before any offer (pre-checked) to install Chrome after the Avast Installation and I have never had Chrome installed on any of the systems I have had during this time. The main reason I have never liked Chrome and had never installed it (still haven't), preferring other browser options.
Now, Avast does have the Avast Secure Browser (ASB) option, a chromium based browser and I have only installed this recently in order to respond on some ASB related topics in the forums.
If installed it will create a desktop icon (if you allow it), but that differs from the Chrome icon.