Nicole Richie (left) and Paris Hilton

'The Simple Life' stars Paris Hilton and Nicole Richie are set to publicly end their two-year-old feud as guests of talk-show king David Letterman.

According to Contactmusic.com, the reality television stars will appear together on an episode of David Letterman's 'The Late Show' in September.

Hilton and Richie have both refused to discuss the reason behind the breakdown of their friendship, with Hilton recently saying: "She knows what she did."

The pair refused to be filmed together for the latest series of their show 'The Simple Life'.