http://upload.wikimedia.org/wikipedia/commons/thumb/a/ab/John_Dillinger_mug_shot.jpg/180px-John_Dillinger_mug_shot.jpg

I believe you're thinking of John Dillinger, the notorious Depression-era bank robber who was shot and killed on July 22, 1934 at the Biograph Theater in Chicago?

You'll find a good bio of him here:
http://www.fbi.gov/libref/historic/famcases/dillinger/dillinger.htm

Wikidpedia gives this accurate account of how his final evening went down: "Dillinger attended the film Manhattan Melodrama at the Biograph Theater in Chicago's Lincoln Park neighborhood. Dillinger was with his girlfriend, Polly Hamilton, and Ana Cumpănaş. Once they determined that Dillinger was in the theater, the lead agent (Samuel A. Cowley) contacted J. Edgar Hoover for instructions, who recommended that they wait outside rather than risk a gun battle in a crowded theater. He also told the agents not to put themselves in harm's way, and that any man could open fire on Dillinger at the first sign of resistance. When the movie let out, Special Agent Melvin Purvis stood by the front door and signaled Dillinger's exit by lighting a cigar. Both he and the agents reported that Dillinger turned his head and looked directly at the agent as he walked by, glanced across the street, then moved ahead of his female companions, reached into his pocket but failed to extract his gun, and ran into a nearby alley. Three agents opened fire, firing five shots. Dillinger was hit from behind and he fell face first to the ground." (link to full article is in my sources list)

The story of Dillinger was recently presented in the movie, "Public Enemies." It's a pretty good film ... directed by Michael Mann and it stars Johnny Depp as Dillinger. I've included a trailer for it below.

Here in Chicago, the Biograph Theater still stands ... it is designated as a historical Landmark in the Lincoln Park neighborhood. Below is a pic of what it looked like then and now :-)