ΛΧΑ was founded in 1909 at Boston University by Warren A. Cole (Boston 1912). The University of Michigan chapter, known as Sigma Zeta among Fraternity members, became the eighth chapter of ΛΧΑ on March 31, 1913.

In the early 1920s, Sigma sold bonds and a since-demolished chapter house at 1511 Washtenaw Avenue to fund construction of the chapter house at 1601 Washtenaw Avenue, which was completed in 1926. In 1976 and ’79, Sigma received ΛΧΑ’s Grand High Alpha Award, which recognizes chapters that maintain superior operations for three consecutive years.

ΛΧΑ became the first fraternity to end pledging when associate membership—a program created by Sigma alumnus George Spasyk ’49 when he was ΛΧΑ’s Executive Director—was adopted in 1972. Associate members can vote, hold office, attend all meetings and Fraternity functions, and wear the letters and regalia of the Fraternity.