Right, Lin. This is from the Internet Movie Data Base.

"As Time Goes By" was written by lifelong bachelor Herman Hupfeld and debuted in 1931's Broadway show "Everybody's Welcome", sung by Frances Williams. It had been a personal favorite of playwright and high school teacher Murray Burnett who, seven years later, visited Vienna just after the Nazis had entered. Later, after visiting a cafe in south France where a black pianist had entertained a mixed crowd of Nazis, French and refugees, Burnett was inspired to write the melodrama "Everybody Comes To Rick's," which was optioned for production by Martin Gabel and Carly Wharton, and later, Warners. Aftr the film's release, "As Time Goes By" stayed on radio's "Hit Parade" for 21 weeks. However, because of the coincidental musicians' union recording ban, the 1931 Rudy Vallee version became the smash hit. (It contains the rarely-sung introductory verse, not heard in the film.) Max Steiner, in a 1943 interview, admitted that the song "must have had something to attract so much attention."

      - Mark