The reaction 63Cu(p,n)63Zn has been studied at bombarding energies between 5 and 11 . 5 Me Y using an activation technique with good energy resolution. Previously unknown levels in 64Zn at excitation energies of approximately 13'37,'13'75, 14'12, 14'3" 14�90' 15�1., 15'6" and 15�77 MeY have been found. It is shown that six of these levels, and the observed absence of levels in some energy regions, can be accounted for in terms of Nilsson's calculations for the single-particle states of a deformed nucleus. If this interpretation is correct, the deformation of 64Zn must be negative, at least in its highly excited states.