Burnham is a village in Cook County, Illinois, United States. The population was 4,046 at the 2020 census. Burnham has a Chicago ZIP code and was named for Telford Burnham, who drew its plat. There are two sections of Burnham. The westernmost section surrounds Torrence Avenue, a north–south street. Torrence Avenue leaves this part of Bu…Burnham is a village in Cook County, Illinois, United States. The population was 4,046 at the 2020 census. Burnham has a Chicago ZIP code and was named for Telford Burnham, who drew its plat. There are two sections of Burnham. The westernmost section surrounds Torrence Avenue, a north–south street. Torrence Avenue leaves this part of Burnham via a bridge, with Chicago on the other side. The eastern section surrounds Burnham Avenue, another north–south street. This section of Burnham ends at Brainard Avenue, where the Hegewisch neighborhood of Chicago lies on the other side. Upon entering Chicago, Burnham Avenue becomes Avenue O.