Paris Hilton and Nicole Richie are set to publicly end their two-year-old feud as guests of US chat show king David Letterman. The beloved TV host has offered to play peacekeeper after inviting The Simple Life stars to appear together on his The Late Show programme in September (06). The two former pals fell out amid reports Richie aired a private viewing of Hilton's controversial sex tape. Both girls have refused to go into detail about their bust-up, with Hilton repeatedly telling journalists, "She knows what she did." Hilton and Richie agreed to team up on TV again for the third season of reality show The Simple Life - but refused to work together onscreen.