Upon arriving in Princeton, McCosh delivered his first speech on the steps of the President's House and immediately endeared himself to the student body by expressing his support for organized athletics. This idea was less popular with some of the conservative Trustees, who frowned on athletics as unduly secular. But McCosh believed that a good education nourished the body as well as the mind, and the first structure built under the McCosh administration was a gymnasium.

Sports at the College of New Jersey to that point had been haphazard at best, with students taking the initiative in most cases. The first gym, little more than a wooden shack, had to be burned down in 1865 after a tramp suspected of carrying smallpox slept there. Despite increasing agitation from the students during the next several years, it was not replaced.

In November 1868, at McCosh's urging, the Trustees commissioned a new gymnasium. The cost of $38,000 was split between two donors, Robert Bonner and Henry G. Marquand, and the building was named in their honor. It was only the second building on the campus to be named for the donor. (Halsted Observatory was the first.) Constructed during 1869, it was dedicated on January 13, 1870.