We present a calculation of the hyperfine splitting of the 2^{3}S state in the ^{3}He atom with inclusion of all QED effects up to α^{3}E_{F}, where E_{F} is the Fermi splitting. Using the experimental value of the 1S hyperfine splitting in ^{3}He^{+}, we eliminate uncertainties from the nuclear structure and obtain the theoretical prediction for ^{3}He of ν_{hfs}=-6 739 701 181(41) Hz, which is in perfect agreement with the experimental value -6 739 701 177(16) Hz [S. D. Rosner and F. M. Pipkin, Phys. Rev. A 1, 571 (1970)PLRAAN0556-279110.1103/PhysRevA.1.571]. This result constitutes a 40-fold improvement in precision as compared to the previous value and is the most accurate theoretical prediction ever obtained for a nonhydrogenic system.