Lyric discussion by NellieWhiskey 

Cover art for Chuck E.'s In Love lyrics by Rickie Lee Jones

Bear with me, because my explanation of Chuck E. (the character) may at first seem irrelevant. Rickie Lee Jones used to be in a relationship with fellow beatnik poet Tom Waits, and they were living in a hotel together. One of the local characters staying there was called Chuck E. Weiss. Chuck helped Waits write some of his album 'Nighthawks At The Diner,' and has since done a little recording of his own. The three - Jones, Waits and Weiss - were good friends, and used to hang out together. After a while, Chuck decided to leave. Some time later, he phoned up the couple at the hotel; Tom answered the phone, and after talking for a brief time, he hung up. Jones asked him who it was, and Waits replied "Chuck E.'s in love." And basically, Jones liked the sound of the phrase.

I read this in a bio on Waits, who is one of my favourite solo artists.