The Chicago Gay & Lesbian Hall of Fame is Wed., Oct. 24, 5:30 p.m., Preston Bradley Hall, Cultural Center, 78 E. Washington, (312) 744-6630. The State of Illinois will host a display based on the Hall of Fame in the lobby of the Thompson Center at 100 W. Randolph Street. On Monday, Oct. 29, and Tuesday, Oct. 30, photos and biographies of the inductees will be shown from 8 a.m. to 5 p.m.