The galaxies in the Revised Shapley-Ames redshift catalog, which is complete to Broughly-equal13, are used to determine the velocity dispersion in the local galaxy field (..nu..<4000 km s/sup -1/). By studying the velocity differences of neighboring pairs of galaxies, we find for the one dimensional velocity dispersion per galaxy sigma = 70 +- 10 km s/sup -1/. (For the three dimensional dispersion, multiply by 3/sup 1/2/; and for the rms velocity difference between pairs, multiply by 2/sup 1/2/.) This velocity dispersion is found in pairs of galaxies irrespective of how isolated they are, and whether or not they are each other's nearest neighbors. The interpretation of isolated galaxy pairs as binaries, whose dynamics is dominated by the two-body force, is therefore questioned. Various implications of the derived velocity dispersion are discussed, with particular attention given to its significance in the virialization process occurring in the cores of the great clusters of galaxies.