Born in Charleston, South Carolina, Gilchrist received an Bachelor of Arts from South Carolina College in 1814 and an Master of Arts from South Carolina College in 1817. He read law to enter the bar in 1818, and was in private practice in Charleston, South Carolina from then until 1831. He was the United States Attorney for the District of South Carolina from 1831 to 1839.
On October 30, 1839, Gilchrist received a recess appointment from President Martin Van Buren to a seat on the United States District Court for the District of South Carolina vacated by the death of Thomas Lee.
Formally nominated on January 29, 1840, Gilchrist was confirmed by the United States Senate on February 17, 1840, and received his commission the same day. He served until his death, in 1856, in Charleston, South Carolina.