New Nubble Space Telescope observations of Cepheid variable stars in the nearby galaxy M96 give a distance to the host galaxy group, Leo I, of 11.6 +/- 0.8 Mpc. This value, used in conjunction with several reliable secondary indicators of relative distance, constrains the distances to more remote galaxy clusters, and yields a value of the Hubble constant (H-0 = 69 +/- 8 km s(-1) Mpc(-1)) that is independent of the velocity of the Leo I group itself.