LETTER TO THE EDITOR: Black string instabilities in anti-de Sitter space

We show how to extend the usual black string instability of vacuum or charged black p-branes to the anti-de Sitter background. The string fragments in an analogous fashion to the Λ = 0 case, the main difference being that instead of a periodic array of black holes forming, an accumulation of `mini' black holes occurs towards the AdS horizon. In the case where the AdS space is of finite extent, such as an orbifold compactification, we show how the instability switches off below a certain compactification scale.