At the critical point of a second-order phase transition, statistical fluctuations are correlated and enhanced in amplitude. We explore this phenomenon in the early universe as a possible mechanism for the formation of galaxies. In an inflationary universe, such dynamical effects on galactic scales are consistent with the constraints imposed by the horizon. Spontaneous breakdown of lepton number provides a model where these ideas are realized. The two-point correlation function for density fluctuations is calculated and agrees with the observed correlation for galaxies. An estimate of the density contrast is shown to be of the required magnitude.