I bought a house with two 30' pecan trees in the backyard. They're only about 12' apart and the branches are definitely overlapping. The trunks are about 20-24" around.

Should I make the tough decision now and chop one down or will they both do ok even though they are that close?

The backyard used to be full of trees, mostly chinese tallow, but the previous owners chopped all of them down except for these 2 pecans. Neither pecan tree has produced any pecans since we moved into the house 2 years ago.

Whichever route you have decided to go is OK. From a landscape standpoint, leaving the two trees might be best. From a pure tree growing viewpoint, one tree is best. Since the trees' roots intertwine and have most likely fussed into one large root system, there will be some stress to the remaining tree for a while. Doing the work now, if you haven't already, is the ideal time to do the work.