A molecular beam spectrometer has been used to observe the hyperfine spectrum and determine the electric dipole moment of the KOH molecule. This EDM had never been measured previously, although theoretical calculations had been made. A refined line shape fitting procedure has helped make possible this determination from the molecular beam hyperfine spectrum. The value of the EDM, which we found for the ground vibrational state, is 7.415+/-0.002 debye. The hyperfine constants, including the potassium nuclear quadrupole, both spin-rotation interactions, and the tensor and scalar spin-spin interactions have been determined for several vibrational states.