David Letterman retiring: Expected to quit in 2015.. announced to his Late Show audience will step down longest-running The Hollywood Reporter Hollywood Reporter announced to his Late Show audience "David Letterman to Retire From CBS' 'Late Show' in 2015" David Letterman retiring: Expected to quit in 2015.. David Letterman retiring: Expected to quit in 2015.. VIDEO... David Letterman retiring: Expected to quit in 2015..