Approximate ab initio Hartree-Fock and first-principles density functional calculations of potential energy surfaces and electronic structures of C60H show that the stable state has H attached to one C atom, outside the buckyball. This C atom is displaced radially outward and is close to being sp3 hybridized. The unpaired electron of C60H is delocalized. The calculated Fermi contact density at the proton is in good agreement with recent low-temperature μSR data. A metastable configuration has atomic H at the center of the ball (H@C60). Once trapped there, H must overcome a large barrier to go through the surface of C60. Other configurations we considered include H attached to one C atom but inside the buckyball, and H bridging one of the two inequivalent CC bonds. The barrier for diffusion of H from outside to the center of C60 have also been calculated. The results are compared to recent muon spin rotation studies in solid C60 and to the states of hydrogen in other forms of carbon.