A supersonic molecular beam of iron monohydride, FeH, has been generated using a laser ablation/chemical reaction scheme and probed at near-natural linewidth resolution by optical Stark spectroscopy utilizing laser-induced fluorescence detection. The observed Stark splitting in Q(3.5) and R(3.5) lines of the F4delta(7/2) <-- X4delta(7/2) (1,0) transition were analyzed to determine values for the magnitudes of the permanent electric dipole moments, absolute value(mu), which were found to be 2.63(3) and 1.29(3) D for the X4delta (v = 0) and F4delta (v = 1) states, respectively. A comparison with ab initio theoretical predictions is made. The lambda doubling in the low-J levels of the F4delta(7/2) (v = 1) state is also modeled.