The kinetics of the gas phase reaction SO3 + NH3 + M were measured in N-2 at 295 K over the pressure range 10-400 Torr with laminar flow reactors coupled to a chemical ionization mass spectrometer. The pressure dependence of the second-order rate coefficient is fit well by the generalized Troe formalism giving k(0) = (3.9 +/- 0.8) x 10(-30) cm(6) molecule(-2) s(-1) and k(infinity) = (4.7 +/- 1.3) x 10(-11) cm(3) molecule(-1) s(-1). The association product of the SO3 + NH3 reaction and secondary acid cluster products were detected by chemical ionization mass spectrometry. Models of the temporal behavior of SO3, sulfamic acid, and sulfamic acid dimer show that sulfamic acid dimerizes at near the hard sphere gas kinetic limit (k > 5 x 10(-11) cm(3) molecule(-1) s(-1), 20 Torr N-2, 295 K) and the dimer is relatively stable with respect to decomposition to monomers (Delta G degrees(298) less than or equal to -9 kcal mol(-1)).