Old Greenwich is a neighborhood/section and census-designated place in Greenwich in Fairfield County, Connecticut, United States. As of the 2010 census it had a population of 6,611. It was founded in 1641.The town of Greenwich is one political and taxing body, but consists of several distinct sections or neighborhoods, such as Banksville, Byram, Cos Cob, Glenville, Mianus, Old Greenwich, Riverside and Greenwich (sometimes referred to as central, or downtown, Greenwich). Of these neighborhoods, three (Cos Cob, Old Greenwich, and Riverside) have separate postal names and ZIP codes.One of the founding settlers of Old Greenwich was Elizabeth Fones, niece and daughter-in-law of John Winthrop, founder and Governor of the Massachusetts Bay Colony. What is now called Greenwich Point was known for much of its early history as "Elizabeth Neck" in recognition of Elizabeth (Fones) Feake Hallet and their 1640 purchase of the Point and much of the area now known as Old Greenwich.