Air carrier landing MDW was informed by ATC that company aircraft awaiting departure had the exact same call sign (flight number); reporter was asked by ATC to question company Dispatch.

Narrative

On short final to Runway 4R into MDW; Tower cleared us to land. They then asked us to confirm our call sign. We did. They then asked the Company Aircraft holding short to confirm their call sign. They had the exact same call sign. Both of us were Company X. After landing; the Ground Controller asked us to contact Company about the confusion. After shutdown I called our Dispatcher. Dispatch said the other aircraft should have been given a different call sign since they were a stubbed flight. Operations was very busy trying to make the schedule work with a large number of aircraft sidelined for maintenance. This somehow slipped through. I'm concerned that our automation didn't catch this at the Dispatch level; and that the Air Traffic Control system accepted it. The fact that it was day VMC with light traffic into MDW made this a non-event. If it had been night IMC; with more traffic; we could have had 2 aircraft on the same runway. Dispatch consoles shouldn't be able to give 2 different aircraft the same call sign while one is still off the gate. I feel this is a technical threat more than any individual.