The energy difference between orthopositronium and parapositronium in the ground $n=1$ state, which is called the hyperfine structure separation $\ensuremath{\Delta}\ensuremath{\nu}$, has been determined in an experiment similar to that of Deutsch, Brown, and Weinstein. The frequency difference between the $M=\ifmmode\pm\else\textpm\fi{}1$ and the $M=0$ Zeeman levels of orthopositronium was measured in a static magnetic field of 8000 gauss at which it is about 2460 Mc/sec. A resonance curve was taken with fixed frequency by varying the magnetic field, and an observed fractional line width, $\frac{\ensuremath{\Delta}{H}_{0}}{{H}_{0r}}$, of about 4.5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}3}$ was obtained. The principal part of the line width (3.6\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}3}$) is due to the annihilation lifetime of positronium; microwave power broadening and magnetic field inhomogeneity account for the remainder. No Doppler broadening is present despite the high velocity of the positronium atoms, because the mean free path of a positronium atom in the gas is small compared to the wavelength of the microwave radiation. The value of $\ensuremath{\Delta}\ensuremath{\nu}$ was computed from the observed values of the frequency and magnetic field at resonance by use of the Breit-Rabi formula to give the result: $\ensuremath{\Delta}\ensuremath{\nu}=(2.0333\ifmmode\pm\else\textpm\fi{}0.0004)\ifmmode\times\else\texttimes\fi{}{10}^{5}$ Mc/sec. The error quoted is 5 times the statistical error and is believed to represent an upper limit to possible systematic errors. The value agrees with the values of Deutsch et al. of (2.0338\ifmmode\pm\else\textpm\fi{}0.0004)\ifmmode\times\else\texttimes\fi{}${10}^{5}$ Mc/sec and (2.0335\ifmmode\pm\else\textpm\fi{}0.0005)\ifmmode\times\else\texttimes\fi{}${10}^{5}$ Mc/sec, obtained with fields of 9500 and 9000 gauss, respectively, and hence confirms the use of the Breit-Rabi formula. The experimental values agree with the theoretical value for $\ensuremath{\Delta}\ensuremath{\nu}$ of 2.0337\ifmmode\times\else\texttimes\fi{}${10}^{5}$ Mc/sec computed to order ${\ensuremath{\alpha}}^{3}$ ry by Karplus and Klein.