We discuss supersymmetric black holes embedded in a Gödel-type universe with cosmological constant in five dimensions. The spacetime is a fibration over a four-dimensional Kähler base manifold, and generically has closed timelike curves. Asymptotically the space approaches a deformation of AdS₅, which suggests that the appearance of closed timelike curves should have an interpretation in some deformation of super-Yang–Mills theory. Finally, a Gödel–de Sitter universe is also presented and its causal structure is discussed.