Substantial electron spin polarization has been observed in low energy electron diffraction (LEED) from the (1) surface of tungsten. The electron polarization is determined by directing a fraction of the elastically diffracted electrons contained within a given LEED beam into a Mott analysis system. An overview of the theoretical background of LEED is given with emphasis on the formalisms developed to calculate the intensities of the beams. The theoretical predictions of electron spin polarization in LEED are reviewed. A short description is given of the experimental technique, and the results of both polarization and intensity measurements on the beam are presented. Polarizations ranging from -35% to +37% have been observed and are shown to depend sensitively on both electron energy and angle of incidence. No similarity was found between the observed LEED polarizations and those predicted theoretically for elastic scattering from free tungsten atoms.