You have a lot of different options, but since you are in Chicago AA may be the simplist. I am not sure that AA flies DFW-LIM an more, but you could certainly go ORD-MIA-LIM very easily. You could also go on CO through IAH, both options are one stop and get you there late evening (10-11 PM). CO flies 757's to LIM, AA has a mixture of widebodies and 757's.

Delta is also another option through ATL. If you are not married to any particular FF program, I would select the airline that has the easiest connections for you.