In the current study we present a potential energy surface(PES) for atomic hydrogen chemisorbed on Cu(110) at Theta =1/8 monolayer (ML) obtained from a plane-wave, gradient-corrected, density functional calculation. This PES is markedly different from and significantly more complex than that predicted by empirical embedded atom method (EAM) calculations. Our results, for example, suggest strongly that the hollow (HL) site is not the preferred binding site for this system. In our calculations, both the short bridge (SB) and pseudo-threefold sites are energetically more favorable than the hollow (HL) site. Energetically, we find the SB site to be slightly lower (30 meV) than the pseudo-threefold site. We also find, however, that the calculated vibrational frequencies for the pseudo-threefold site agree more closely with experimental electron energy loss data than for the SB site. In view of the relatively flat region between adjacent pseudo-threefold sites along the cross-channel [001] direction, we speculate that the hydrogen atom motion at low coverages may be two-dimensional rather than quasi-one-dimensional in character.