The reaction between atomic nitrogen and H-2 has been studied in order to elucidate the mechanism of NH3 formation on Rh(111). Atomic nitrogen layers of 0.10 monolayer (ML) coverage were obtained by adsorbing NO at 120 K and selectively removing the atomic oxygen from dissociated NO by reaction with H-2 at 375 K. The rate of NH3 formation is first order in the atomic nitrogen coverage and linearly proportional to the H-2 pressure below 5 x 10(-7) mbar. Static secondary ion mass spectrometry (SSIMS) indicates that N and NH2 are the predominant reaction intermediates, while small amounts of NH3 are also detected. The NH2 surface coverage increases with increasing H-2 pressure. The presence of NH2 is also indicated by the appearance of a reaction-limited H-2 desorption state in temperature-programmed desorption (TPD) spectra. The hydrogenation of NH2 to NH3 is expected to be the rate-determining step in the NH3 formation. From the temperature dependence of the NH3 formation rate an effective activation energy of 40 kJ/mol was determined, which could be translated into an activation energy of 76 kJ/mol for the hydrogenation from NH2 to NH3.