The real issue is not that Avast is offering to install Chrome for you,
but that that install is pre-checked, (default opt-in) rather than you opt-in as you would if the install box was not pre-checked (Avast offers the box and if you want it, you must check the box to have it installed).
In other words, all default installs by Avast are pre-checked to install where you must uncheck anything you don't want. All default opt-in, to defeat, you must opt-out. Use custom install.
A good program to prevent auto-installs commonly found on free programs:
https://unchecky.com/