The Zeeman effect on the F-1/2<--3/2 hyperfine component of the R (0) line in the (0,0) band of the A(1) Pi-X(1) Sigma(+) transition of iridium mononitride, IrN, was investigated using a supersonic molecular beam optical spectrometer. The magnetic g(J)-factor for IrN in the A(1) Pi state was determined to be 0.96+/-0.05. The general applicability of Zeeman measurements is described and the g,-factor which is determined is related to plausible molecular orbital descriptions for IrN in the A(1) Pi state.