Promethean Everlasting Matches were matches made of Umbeka wood. The heat from the flame made the wood grow as fast as the flame consumed it, so the match would never burn down. They were created by the Eternity Perpetual Company on the planet Umbeka. (PROSE: The Cabinet of Light, The Resurrection Casket) Some were made so that they gave off a lemon scent when lit. (PROSE: Venusian Lullaby)
In his first incarnation the Doctor often carried a box of these matches. (PROSE: Time and Relative, Venusian Lullaby) He once claimed to have invented them himself. (PROSE: The Exiles) Ian Chesterton made reference to the matches when retelling the story of how he first met the Doctor and the Daleks. (PROSE: Doctor Who in an Exciting Adventure with the Daleks)
The Seventh Doctor kept everlasting matches in the Jade Pagoda. (PROSE: Sanctuary) The Seventh Doctor also used everlasting matches to light his way in WWII-era London when conventional lighting was unavailable due to the Blitz. (PROSE: Illegal Alien) He gave some everlasting matches to a clerk in Valhalla during a power cut. (AUDIO: Valhalla)
Behind the scenes
Everlasting matches were first mentioned in the first Doctor Who novelisation, Doctor Who in an Exciting Adventure with the Daleks by David Whitaker. The Eternity Perpetual Company was first mentioned in TV: Carnival of Monsters.