Greenville is a home rule-class city in Muhlenberg County, Kentucky, in the United States. It is the seat of its county. The population was 4,312 at the 2010 census.
The town was settled in 1799 on an estate donated by local landowner William Campbell in order to establish a seat of government for a new county. Greenville was not established by the state assembly until 1812, however. It was incorporated as a city in 1848.
The city was probably named for the Revolutionary War general Nathanael Greene. Local lore holds it was named by Campbell's wife after the abundant forests seen from the town's hilltop location.
Greenville is located at 37°12′26″N 87°10′35″W (37.207158, -87.176499).
According to the United States Census Bureau, the city has a total area of 4.8 square miles (12 km2), of which 4.8 square miles (12 km2) is land and 0.21% is water.
As of the census of 2000, there were 4,398 people, 1,859 households, and 1,217 families residing in the city. The population density was 921.7 people per square mile (356.0/km²). There were 2,047 housing units at an average density of 429.0 per square mile (165.7/km²).