  Relativistic corrections to the hyperfine splitting are calculated for the
triplet $2^3S_1$ state of the helium isotope He$^3$. High precision variational
wave functions are employed, where the electron-electron correlations are well
accounted for. Due to the unknown nuclear structure a comparison with the
experimental result is performed via He$^{3+}$ hyperfine splitting.
Surprisingly, the second order contribution due to Fermi interaction, in spite
of the additional small factor $m/M$, is very significant.
