Periodic, self-consistent density functional theory (DFT-GGA, PW91) calculations are used to study the reaction mechanism for nitric oxide (NO) reduction by hydrogen (H) on Pt(100). Energetics of various N-O activation paths, including both direct and hydrogen-assisted N-O bond-breaking paths, and the formation of three different N-containing products (N, NO, and NH), are systematically studied. On the basis of our analysis, NO* dissociation has a lower barrier than NO* hydrogenation to HNO* or NOH*, and therefore, the direct NO dissociation path is predicted to dominate N-O activation on clean Pt(100). The reaction of atomic N* with N* and NO* is proposed as the mechanism for N and NO formation, respectively. NH formation from N* via three successive hydrogenation steps is also studied and is found to be kinetically more difficult than N and NO formation from N*. Finally, NO adsorption phase diagrams on Pt(100) are constructed, and these phase diagrams suggest that, at low temperatures (e.g., 400 K), the Pt(100) surface may be covered by half a monolayer of NO. We propose that high NO coverage might affect the NO + H reaction mechanism, and therefore, one should explicitly take the NO coverage into consideration in first-principles studies to determine the reaction mechanism on catalyst surfaces under reaction conditions. A detailed analysis of high NO coverage effects on the reaction mechanism will be presented in a separate contribution.