The song was written by Chrissie Hynde, the leader and singer of The Pretenders, and included on that band's 1980 debut album Pretenders. The same year the track was covered by Grace Jones on her first post-disco album Warm Leatherette, recorded at the Compass Point Studios in the Bahamas with among others Sly and Robbie. In the liner notes to Island Records' 1998 compilation Private Life: The Compass Point Sessions, Hynde is quoted as saying:
Like all the other London punks, I wanted to do reggae, and I wrote "Private Life". When I first heard Grace's version I thought 'Now that's how it's supposed to sound!' In fact it was one of the high points of my career - what with Sly and Robbie being the masters, and Grace Jones with her scorching delivery. Someone told me it was Chris Blackwell's idea - thanks Chris![1]
Wikipedia: Private Life (song)