After the Student Army Training Corps program ended with the cessation of hostilities in World War I, an organization was formed on the rain soaked campus of Case School of Applied Sciences that was called the Iroquois Club. For several years the club lived in complete secrecy until firmly established. In the autumn of 1922 a modest house was rented at 2085 Cornell Road, Southeast, and the name of the society became Tau Gamma Psi, a local fraternity no longer operating in secret so that it could petition the Phi Kappa Tau Fraternity for membership; that same year, the petition was rejected. Negotiations with Phi Kappa Tau extended over the course of three years. For most of this period there was a feeling within the national fraternity that expansion should exclude any additional chapters in Ohio. However, after rapid growth and intense lobbying from supporters in the Cleveland alumni association and on the Case faculty, the 1924, Detroit, Michigan, Fourteenth Annual Convention unanimously granted the petition of Tau Gamma Psi on August 29, 1924.

Alpha Delta was to be installed and become the twenty-eighth chapter (and the fifth Ohio chapter) to be granted a charter by the national fraternity between January 29 and 31, 1925. Alpha Delta chapter had thirty-nine charter members who were initiated by officiating members Grand President John V. Cotton, Grand Secretary Ralph K. Bowers, and other members of the degree team on January 30, 1925. Also present were Doctor Henry E. Hoagland of the grand council, O. M. Stone, E. G. Gossett, and C. C. Goddard of the Cleveland alumni association. The following afternoon, Alpha Delta chapter was presented its charter and the ceremonies were concluded that evening with a formal banquet and dance at Fenway Hall Hotel, at which Guy R. Pratt was the toastmaster. The initiated president of Alpha Delta chapter was Harry Yates George and the initiated secretary was Ernest A. McLeod. Alpha Delta's graduate council president was Stanley T. Gridley and the secretary was Jasper W. Avery.

After cleaning out and giving up the Bellflower residence to Case’s Sigma Chi chapter, Alpha Delta moved into a modern, four-story house built on the south side of the campus of the newly merged Case Western Reserve University in 1968. Unfortunately, after some years of gradual deterioration in scholarship and the building of monetary problems within the chapter, Alpha Delta ceased operations on the Case Western Reserve campus in 1992. The official reasoning was "squatting" by members of the chapter, brothers living in the house without making payments for their stay.

In the autumn of 1998, national expansion consultants Jeff Anderson (of Alpha Kappa chapter) and Carlos Salazar (of Alpha Pi chapter) set about to reestablish a colony on Case Western Reserve's campus. They enlisted the help of the fraternity's former advisor, Doctor Ignacio Ocasio, and a Beta Chapter alumnus, Doug Brown, to advise the colony that was forming. Eleven male students, primarily freshmen, were associated on the eve of the colonization, October 8, 1998. Shortly after the ceremony, nearly fifty people attended the colonization banquet. The banquet was an affair which well exceeded the allotted budget, but introduced the Alpha Delta colony in a style to be remembered. The colony was officially recognized by the campus Inter Fraternity Congress on February 26, 1999, when it presented itself to the Inter Fraternity Congress and representatives from the Pan-Hellenic Council and was conferred colony status by an Inter Fraternity Congress vote. During the spring of 2000, the national fraternity accepted the colony's petition to be inducted as a full chapter. As a result, on May 11, 2000, staff from the national fraternity along with brothers from the Baldwin-Wallace Chapter initiated twenty-three of the associate members over the course of six hours. The next day, May 12, 2000, the group was ceremoniously inducted as the Alpha Delta chapter of the Phi Kappa Tau Fraternity at a large banquet, attended by nearly the entire staff of the national fraternity, parents, friends, and important Case Western Reserve staff, all who came to witness two years of effort come to fruition.