The Minister of Chance was one of only five Time Lords who survived the Second War in Heaven and the destruction of Gallifrey. (PROSE: The Gallifrey Chronicles)
Behind the scenes
Beyond the above appearance in a story this wiki considers a valid source, the Minister of Chance was also seen in the webcast, Death Comes to Time
The character model for the Minister of Chance in Death Comes to Time was clearly based on his portrayer, Stephen Fry.
In this extra-continuous story, the Minister thwarted General Tannis' plans to infect the planet Alnelan with a deadly plague, but the Minister's female assistant 'wandered off' on the planet.
Following his defeat Tannis agreed to the Treaty of Karselai and signed away any rights to alien planets. Despite this, the Canisian military, led by Tannis, brutally conquered the Santine Republic, confining the leading members of the Republic to a prison camp. The Minister, who was able to transfer a virus to a Canisian computer via speech, took the place of a version of the Doctor in seeding a rebellion on Santiny while the Doctor investigated the deaths of two Time Lords on Earth. Tannis was also working towards wiping out the last members of the Fraction and by massacring the Santine prisoners he provoked the Minister into breaking the rules about non-interferance, forcing the Doctor to confront the Minister and revoke his TARDIS.
The character would then go on to headline his own audio series, albeit one in which he was played in regenerated form by Julian Wadham rather than by Stephen Fry. This eponymous series, though, is quite explicitly not set in the DWU and is in no way covered by this wiki.