Bresse, region, in Burgundy, E France, between the Ain and Saône rivers. Bourg-en-Bresse is the historic capital. A fertile farm area, it is famous for its chickens and wines. To the south is the Dombes, a region dotted with thousands of ponds, partially drained and reclaimed. Bresse was part of the duchy of Savoy until 1601, when it was ceded to France along with Bugey (a district between the Ain and the Rhône) and the Territory of Gex. All three were added to Burgundy prov.