Quenchers? I haven't been there in a while, but I don't remember it being loud, and they do have a great beer selection.
Quenchers
2401 N Western Ave
Chicago, IL 60647-2011
(773) 276-9730
There was a time when I was at Quenchers at least once a week. It was always my "quiet place", so I think it should fit the bill for you. They often have live music, but it's in an adjacent room so it's usually not a problem. There's around 200-300 beers there, and they hold numerous "fests" throughout the year, highlighting IPA's, stouts, and sour beers.
I would also venture a bar/restaurant for your query - Jerry's on Division. They've got a very, very extensive beer list, with a lot of rare 22oz and cool stuff on tap. They also do pitchers, which is a good volume-for-dollar proposition. Food is hit or miss, but I've never been disappointed with beer there. And, its definitely easy to hold a conversation there.
Jerry's Sandwiches
1938 W Division St
Chicago, IL‎
(773) 235-1006‎