[1][2] The oldest building on the square is the Ann Hamilton House, at 26 East Bryan Street, which dates to 1824.

Following vandalism of the cemetery by occupying Union forces during the Civil War the location of Greene's burial was lost.

The cornerstone of the monument was laid by Gilbert du Motier, Marquis de Lafayette, in 1825.

In fact, due to financial restrictions the unmarked obelisk served for several years as a joint monument to both Greene and Casimir Pulaski.

Christ Church Episcopal occupies the southeastern trust lot of the square at 28 Bull Street.

Early clergy of the church include John Wesley and George Whitefield.