We present a computer simulation study on the crystalline phases of hard ellipsoids of revolution. For aspect ratios >= 3 the previously suggested stretched-fcc phase [Frenkel and Mulder, Mol. Phys. 55, 1171 (1985)] is replaced by a different crystalline phase. Its unit cell contains two ellipsoids with unequal orientations. The lattice is simple monoclinic. The angle of inclination of the lattice, beta, is a very soft degree of freedom, while the two right angles are stiff. For one particular value of beta, the close-packed version of this crystal is a specimen of the family of superdense packings recently reported [Donev , Phys. Rev. Lett. 92, 255506 (2004)]. These results are relevant for studies of nucleation and glassy dynamics of colloidal suspensions of ellipsoids.