The White Sox signed Paul Konerko, their own free agent first baseman, to a three year deal for something around 37 million. This is on top of signing Adam Dunn, presumably to split time at first and DH with Konerko, and resigning AJ Pierzynski.
The Cubs, meanwhile, signed Carlos Pena, a LH first baseman with some power, from the Tigers. He hit only .196 last year (but had a .340 OBP), and apparently this is good enough for a 1 year 10 million dollar deal.
The Cubs are also said to be interested in dealing for Matt Garza, whom the Rays would apparently like to trade for prospects.