The zero-field hyperfine structure of the metastable 23S1 state of He3 has been measured by the optical pumping magnetic resonance method. The hyperfine transitions in a weak magnetic field were observed at low temperature in order to achieve narrow linewidths. Discussions of the theory of the hyperfine structure, the theory of the experiment, the apparatus, and the experimental procedure are presented. The final value for the hyperfine structure is 6739 701177 +/- 16 Hz on the A-1 time scale. The fractional pressure shift of the hyperfine structure is (-7.4+/-3.0)×10-9/Torr. The theoretical and experimental values for the hyperfine structure are compared, and the dependence on the nuclear structure is discussed.