Built in 1913 on the rear of a lot owned by Junius D. Webb since 1894 (his former house is at 302 Pittsboro Street).
Said to have been constructed from parts of the demolished "First President's House" that once was located on East Cameron Street on UNC's campus, and that was demolished in 1913 to make way for Swain Hall.
Some kind of legal action (likely about the estate/will of Junius Webb, who died in 1931) required the selling of the property in April 1943. Owned by W. A. Ector from April 1943 to April 1943 (yes, those dates are correct). Owned by W. G. and Minnie Fields from April 1943 to 1944. Owned by Jesse and Josephine Cole from March 1944 to 1952. Owned by Charles and Kathryn Bream from August 1952 to 1971.
Since February 1971 it has been owned by the Roman Catholic Diocese of Raleigh, and is used as a home for its local bishop(s).
April 18, 1952 article (via CHW)
View south, 1994 (photo by Jason D. Smith, via Carolina Alumni Review)
View south, June 2019 (via Google Streetview)
From the West Chapel Hill Historic District NRHP form:
Called by some sources the "First President's House," portions of this structure were salvaged from the "President's House," which dated from c.1795 to 1840 and was demolished to make way for Swain Hall at Columbia Street and Cameron Avenue. The salvaged portions were incorporated into new construction by Junius D. Webb on his back lot ca. 1913. In its present configuration, the Caldwell-Mitchell-Webb House is much altered by the application of aluminum siding but, in profile, it suggests a nineteenth-century hipped-roof I-house form. lt features an irregularly spaced three-bay fenestration, with double-hung windows (probably dating from the early twentieth century), an entry transom, an interior chimney and a hipped wrap-around porch with turned spindles.