Greene is a village in Chenango County, New York, United States. The population was 1,580 at the 2010 census. The village is named after General Nathanael Greene. It is within the town of Greene and is northeast of Binghamton.

Chenango County is a county located in the south-central section U.S. state of New York. As of the 2020 census, the population was 47,220. Its county seat is Norwich. The county's name originates from an Oneida word meaning 'large bull-thistle'. The county is part of the Southern Tier region of the state.