The title of the song was originally "Sex Offender." Bassist Gary Valentine originally wrote the song about an 18-year-old boy being arrested for having sex with his younger girlfriend. Debbie Harry changed the lyrics so that the song was about a prostitute being attracted to the police officer that had arrested her. The track was produced by Richard Gottehrer who had worked with 1960s girl group The Angels and the song is reminiscent of that era in its style.
Private Stock insisted that the name of the single be changed to "X-Offender" because they were nervous about the original title. It was released in 1976 with the B-side being "In the Sun". The song didn't chart but Chrysalis heard it with the Blondie album and signed the band. "X-Offender" was later the B-side to "Rip Her to Shreds." Due to the limited copies of the single released and the subsequent popularity of the band, a copy of the original US Private Stock single "X-Offender"/"In the Sun" is a sought-after rarity with copies selling for £750 in collectors' markets since the mixes of both songs on the single are different from those on the Blondie album. These mixes appear as bonus tracks on EMI/Capitol Records' 2001 re-issue of the album. Unfortunately no master tapes of the Private Stock versions have been kept in the archives, subsequently these bonus tracks are direct transfers from vinyl.