We calculate over 1500 ab initio points for the HO2- ground state at the QCISD(T)/6-311++G(2df,pd) level for a wide range of geometries. We fit these points to a 120-parameter analytic function to obtain a potential energy surface (PES) valid for large amplitude hydrogen motion. We then calculate and assign vibrational energy levels for this PES. There is intramolecular proton transfer when the hydrogen atom tunnels through a T-shaped transition state separating the two equivalent equilibrium geometries. The O-O distances are very different for the equilibrium and transition state geometries and the proton transfer is truly multidimensional. When there is nuclear tunneling the vibrational levels are split and we focus on levels with significant splitting. The barrier to proton transfer is 6058 cm(-1) (4752 cm(-1) with zero-point correction). Significant splittings are observed for relatively low-lying vibrational levels that may be experimentally accessible. Results are presented for H-O-16-O-16 and H-O-17-O-17. For H-O-16-O-16 the first three levels with splitting greater than 10 cm(-1) are, in order of increasing energy, (0,2,3), (0,1,5), and (0,3,2) where v(2) is the O-O-H bend quantum number and v(3) is the O-O stretch quantum number. The (0,4,0) level lies between the (0,2,3) and (0,1,5) levels but the splitting is only 6 cm(-1) showing that although H-O-O bend excitation is essential, O-O stretch excitation greatly facilitates proton transfer. This is not because it permits tunneling at a smaller O-O distance than that for the equilibrium geometry. Rather, it is because it permits tunneling at the,larger O-O distance corresponding to the transition state geometry.