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By the intermediate value theorem, there is a regular dodecahedron in hyperbolic 3-space whose dihedral angles are all $90^\circ$. (The angles for a Euclidean regular dodecahedron are greater than $90^\circ$ and the angles for an ideal regular dodecahedron are $60^\circ$.) The group generated by the reflections in the sides of this dodecahedron is a discrete group $\Gamma$ with the property that $\mathbb{H}/\Gamma$ is contractible, since it's just a copy of the dodecahedron.