I have a theory that I tested out. It truly is them trying to push Chrome on you. I completely uninstalled using Revo Uninstaller, then reinstalled from the site download. That download AUTOMATICALLY installs Chrome without asking. I let Chrome stay on and restarted the computer several times. No popup. Then last night before I shut down, I uninstalled Chrome using Revo. This morning, the popup was back with the two boxes checked.
I believe Avast scans to see if you have Chrome, and if you don't, it gives you the popup. First, I'm upset that it installed Chrome without my consent, and second, I'm sick of Google trying to insert itself into every part of my life without asking, so I'm uninstalling Avast and going to the Windows virus scanner.
I know you have to pay the bills, but seriously, this is an intrusion of my privacy and there are enough of those already what with Comcast now scanning to see if I'm downloading anything illegally. If I wanted to use things illegally, I wouldn't have this problem because I would have downloaded a cracked version of Avast!
I hope you enjoy the money Google is paying you. I know you have to stay in business, but getting into bed with the evil king of the internet is not (IMHO) how to do it. Seriously, if you just charged $1 for the free version, you'd make that money up quickly. I'd gladly pay it. If you lie down with dogs, you wake up with fleas, Avast....or worse...worms!
BTW, Google Chrome spies on you from the program that installed it, even if Chrome itself is not running. Goodbye, Avast. It was nice while it lasted.