The first class included about 30 children of Irish, Polish, German and Italian working-class immigrants. The first classrooms were located in a three-story house in the Oak Lawn neighborhood. By 1925, a red-brick building was built for the school at its current location near the Oak Lawn-Blackburn intersection. In 1947, the building was expanded and gold brick was placed over the red so that the structure would match the church's façade. The school has kept most of its original architectural details, such as high ceilings, arches and hardwood cabinetry. In 1963, HTCS became the first elementary school in Dallas to earn accreditation, which it maintains today.

Located in the heart of Dallas, HTCS today has more than 200 students and offers classes from preschool to eighth grade under the guidance of a faculty and staff of 24 education professionals. Sixty percent of the faculty has advanced education placing the school seventh out of 95 area private schools with faculty that have Master's and Doctor's degrees.

Ninety-four percent of HTCS graduates go on to attend local private high schools at the nation's top universities including The Citadel, Columbia, Fordham, Southern Methodist University, Stanford, The U.S. Naval Academy and Vanderbilt.