A numerical model of the excitation of ammonia in dense interstellar clouds predicts strong maser emission in various inversion doublet lines when infrared pumping to the lowest vibrationally excited state is included. Specifically the (6, 3) transition mases, while the (5, 3) and (4, 3) transitions are in normal emission, as observed in W51. Model conditions are H-2 density between 10(8) and 10(10) cm-3, NH3 column density 10(18) cm-2, and infrared temperature greater than 200 K, comparable with conditions required for OH and H2O masing in regions of star of star formation. The intensity of the maser emission depends on the infrared field, suggesting that time variations may be due to fluctuations in an infrared source. Detailed modeling of the other ammonia maser lines awaits the calculation of more collision cross sections.