This chapel opened in 1766 as an extension of Trinity Church, which is slightly farther down Broadway. Unlike Trinity Church, St. Paul's was saved from the Great Fire by local bucket brigades. The original building still stands today, making it one of the oldest churches in Manhattan.
During the revolution, St. Paul's was known for Loyalist leanings. It's Episcopalian, which is a subset of Anglican, which you'll remember is the 'Church of England' - you can probably guess whose side they were one. Church services specifically prayed for the King and Royal Family, which you can imagine wasn't too popular with the revolutionaries who were occupying the town in 1776.
After the war ended there was a turnaround in the Church's politics. The rector and some of the more Loyalist congregants left New York, and it became more Patriot-friendly. George Washington attended a service here on his inauguration day, and kept attending while he lived in New York - which probably went a long way toward repairing the church's reputation among the Patriot population.