this is from their website
The Past
Founded as the Greenock Mission in 1808, St Mary's is the oldest Catholic parish in the town, and is the "mother" of many parishes on Lower Clydeside. The first "Mission Rector", Rev. John Davidson, rented the Star Hall to celebrate Mass for a congregation of about 100. Our parish records date from his arrival, the first entry being the marriage of a soldier named Peter Gavie, to Elizabeth Collins, on 16 November 1808.
Even earlier, M. Capron, a French priest fleeing from the Revolution, was, as far as we know, the first resident priest in Greenock since the Reformation. By 1798 he had established his "French Academy" in the "town of ships and sugar".
The first St. Mary's Church, in East Shaw Street, was opened in 1816 by Bishop Cameron. In his sermon he "expressed his most grateful acknowledgments for the tolerance in matters of religion now so conspicuous in the country", and stressed "the mutual obligations which bind man to his fellow-man."
On August 17, 1862 the present church, designed by George Goldie of London, was completed at a cost of £6,000. Seating 800, it was hailed as "one of the finest churches in Scotland".