Moncure, founded in 1881, is a small rural unincorporated community in southeastern Chatham County, North Carolina, United States. Moncure and the neighboring community of Haywood form the Moncure census-designated place, which had a population of 711 at the 2010 census. The community is located near the confluence of the Deep and Haw river…Moncure, founded in 1881, is a small rural unincorporated community in southeastern Chatham County, North Carolina, United States. Moncure and the neighboring community of Haywood form the Moncure census-designated place, which had a population of 711 at the 2010 census. The community is located near the confluence of the Deep and Haw rivers, which form the Cape Fear River. Moncure once served as the westernmost inland port in the state, linked to the Atlantic Ocean by steamships.