  We investigated the tunneling anisotropic magnetoresistance (TAMR) in thick
hcp Co films at cryogenic temperatures using scanning tunneling microscopy. At
around -350 mV, a strong TAMR up to 30\% is found with a characteristic voltage
dependence and a reversal of sign. With the help of \textit{ab initio}
calculations the TAMR can be traced back to a spin-polarized occupied surface
states that experience a strong spin-orbit interaction leading to a
magnetization direction depending hybridization with bulk states.
