This is the B-side to "Why Don't They Leave Us Alone," which is a cool song too but readily available on Youtube.
Here's Carl's wiki page. I didn't know anything about him when I picked this up from Vintage Freak today for a dollar; I just liked the song title because of the word "chump." It's on Back Beat, a Houston label that operated from 1957 to 1974.
Download: I Won't Let That Chump Break Your Heart