Pressure broadening of the (J,K) = (1,1), (2,2), and (3,3) inversion transitions of NH3 was measured using normal- H-2 as the broadening agent at kinetic temperatures of 15 to 40 K. Measurements were taken in a quasiequilibrium cell using the collisional cooling technique. H-2 pressure broadening cross sections were compared to low-temperature He pressure broadening of the same transitions and found to be from 2.5 to 8 times larger than corresponding He cross sections. Measured normal- H-2 and He cross sections were also compared to calculated J = 0, para-H-2 cross sections.