They competed via the Internet. The sheriff says it's something that's never been done before.
The Cook County Jail's chess program launched in April 2012. So far, roughly 600 detainees have taken part.
Dart says the goal is to teach them the importance of patience, diligence and critical thought.
"A lot of people, their whole life has always been a reactionary type of life where they just live second by second," said Dart. "This builds into you this concept that you need to think well beyond what's happening that second."
The Russian team won the tournament. Those players will receive a certificate from world chess champion Anatoly Karpov.
After the match, Karpov identified one of the Cook County detainees as the most distinguished competitor on either side, having won both of his games -- including one in just three moves.