How to cut chicken without producing loud noises
Plan a bit ahead. Move the chicken from the freezer to the fridge the night before, so it's thawed (or at least not rock-hard) when it's time to cut it. Or if for some reason that won't work, thaw it at least partially under running water.

Beyond that, make sure your knife is sharp, so you're not having to spend more effort than you should. With thawed meat and a sharp knife, you shouldn't need violent swings of your knife.

To answer the actual question you asked, a kitchen towel (or several layered) will dampen impact on the counter some. And you might find that different parts of the counter rattle less, or even try cutting on your table. But I'd really suggest avoiding having to whack it hard enough to make the counter shake in the first place!