West Chapel Street came into being as the in-town portion of the Chapel Hill Road, which predated Durham-proper. The roadway that is now Chapel Hill Street was known as Green Street on the north/east side of the railroad tracks, and Chapel Hill Road to the west/south. As the town organized, the in-town portion of the old roads were given the "street" suffix, and West Chapel Hill Street was such until it turned to the southwest ~1 mile to the west of Five Points.
Chapel Hill Street is unique in downtown for having its east-west split at Five Points rather than at Mangum Street. There was therefore a very small section of West Chapel Hill Street (between the RR and Five Points,) that was previously part of Green Street (as was all of East Chapel Hill St.,) named after John Ruffin Green, who is well known for his part in the famous soliders-at-the-bennett-place-raid-the-tobacco-warehouse story of how brightleaf tobacco was spread around the country. (It was his factory.) At the time, (1865) Green owned a large area of land on the north side of his eponymous street, west of what would become Morris Street. His house was located at the intersection of Green Street and Peabody Street (north side,) next to the railroad tracks. Southwest of Peabody St. / the Hillbsorough Road / RR tracks, Green's land extended - known as Green Woods.
Green Street was renamed sometime between 1898 and 1902, when it was renamed East Chapel Hill Street (east of Five Points) and West Chapel Hill Street (west of Five Points.)
West Chapel Hill Street (and Chapel Hill Road) was one of Durham's streetcar streets.