In this talk, I will present a new supersymmetric compactification of M-theory to a three-dimensional Gödel universe. First, I give a historical motivation and discuss how our setup connects to the work of Gaiotto, Strominger, Yin and collaborators, who showed how counting certain probe brane states give rise to the entropy of a D4-D0 black hole. In the M-theory picture, the probe branes move in a flux-supported background $AdS_3 \times S^2 \times CY_3$. Then I discuss the effect of the gravitational and electromagnetical backreaction of the probe branes on the background: the $AdS_3$ factor is drastically changed to a three-dimensional Gödel universe. Finally, I explain some properties of this solution and discuss remaining issues, as why this system fails to describe black hole microstates.