I think I *may* have found the cause of and then solved the problem.
I'm running Win7 so this may or may not apply to other OS's, but I suspect it will work at least for all Windoz users.
The cause is a file named Offers.ini located in Program Files/AVAST Software/Avast/Setup/ . Yeah, it's not easy to find. If you look inside (it's a text file and Notepad opens it nicely) you can see a whole list of potential offers with variables that indicate whether or not you were silly enough to say "yes." Unfortunately I could not edit or rename it, even when I logged in as Administrator. Not sure how Avast! managed that little trick.
However, despair not! I found a workaround. I found the Avast! icon in my "Show hidden icons" box, right clicked on it and selected Update> and selected Program. Avast! then updated the program and asked to reboot the computer. I allowed it to do so and on rebooting, Avast brought up a box which said "Almost Finished" and that box had a checked box beside a question, "Do you want to install Google Chrome?" I carefully UN-checked the box, then clicked on Finish.
I then rebooted the computer and voila no more pop-up Chrome!!!!
I investigated the mysterious Offers.ini file and discovered that the variables attached to [Google Chrome] had been changed.
So: At least for me that file was the problem, and it could be fixed by updating the program and being careful with checkboxes.
I hope this works for others.