We have carried out a multi-fractal analysis of the distribution of galaxies in the three Northern slices of the Las Campanas redshift survey. In this analysis we have studied the scaling properties of the distribution of galaxies on length scales from 20 h⁻¹ Mpc to 200 h⁻¹ Mpc. Our main results are: (1) The distribution of galaxies exhibits a multi-fractal scaling behaviour over the scales 20 h⁻¹ Mpc to 80 h⁻¹ Mpc, and, (2) the distribution is consistent with homogeneity on the scales 80 h⁻¹ Mpc to 200 h⁻¹ Mpc. We conclude that our results are consistent with the Universe being homogeneous at large scales and the transition to homogeneity occurs somewhere in the range 80 h⁻¹ Mpc to 100 h⁻¹ Mpc.