COPA and American Airlines have round-trip flights from Chicago (ORD) to Lima, Peru (LIM) for $301-$368 with a connection. Flights in November, January, February, and March. 7-day minimum stay required.
A Carry-on bag and also a personal item is allowed for free on American. COPA has additional bag fees. You can avoid paying for seat selection by accepting the randomly assigned seat at the gate.