On May 23, 2010, the Braves lost against the Pirates. The only starting position players from that game still on the team are Martin Prado and David Ross. Nate McLouth led off. Troy Glaus hit cleanup. Melky Cabrera was hitting sixth with a .570 OPS. It's weird to look at the box score.
It was also the last time that the Braves lost a game Kris Medlen started.
There are some caveats: Medlen missed a year with Tommy John surgery, and he's spent a lot of time in the bullpen, both before and after the surgery. But even if you ignore the actual dates, we're still talking about 22 starts. The last 22 games Medlen started, the Braves have won.
If you're thinking that might be something close to a record, you're exactly right. It ties the MLB record held by Carl Hubbell and Whitey Ford, with Medlen passing up Roger Clemens and Lefty Grove on the list.