We report on the first determination of the distance to the Coma Cluster based on surface brightness fluctuation (SBF) measurements obtained from Hubble Space Telescope WFPC2 observations of the bright E0 galaxy NGC 4881 in the Coma Cluster and ground-based observations of the standard E1 galaxy NGC 3379 in the Leo-I group. Relative distances based on the I-band fluctuation magnitude, I(SBF), are strongly dependent on metallicity and age of the stellar population. However, the radial changes in the stellar populations of the two giant ellipticals, NGC 3379 and NGC 4881, are well described by published Mg_2 gradients, and the ground-based measurements of I(SBF) at several radial points in NGC 3379 are used to calibrate I(SBF) in terms of the Mg_2 index. The distance to NGC 3379, assumed to be identical to the average SBF distance of the Leo-I group, is combined with the new SBF measurements of NGC 4881 to obtain a Coma Cluster distance of 102+-14 Mpc. Combining this distance with the cosmic recession velocity of Coma (7186+-428 km/s), we find the Hubble constant to be H_0 = 71+-11 km/s/Mpc.

12 pages, LaTex, includes aaspp4.sty and 3 eps figures. To appear in ApJ Letters