  We report on the first experimental results for microwave spectroscopy of the
hyperfine structure of antiprotonic He-3. Due to the helium nuclear spin,
antiprotonic He-3 has a more complex hyperfine structure than antiprotonic He-4
which has already been studied before. Thus a comparison between theoretical
calculations and the experimental results will provide a more stringent test of
the three-body quantum electrodynamics (QED) theory. Two out of four
super-super-hyperfine (SSHF) transition lines of the (n,L)=(36,34) state were
observed. The measured frequencies of the individual transitions are
11.12559(14) GHz and 11.15839(18) GHz, less than 1 MHz higher than the current
theoretical values, but still within their estimated errors. Although the
experimental uncertainty for the difference of these frequencies is still very
large as compared to that of theory, its measured value agrees with theoretical
calculations. This difference is crucial to be determined because it is
proportional to the magnetic moment of the antiproton.
