As part of the survey component of the Megamaser Cosmology Project, we have discovered a disk megamaser system in the galaxy CGCG 074-064. Using the Green Bank Telescope and the Very Large Array, we have obtained spectral monitoring observations of this maser system at a monthly cadence over the course of two years. We find that the systemic maser features display line-of-sight accelerations of ~4.4km/s/yr that are nearly constant with velocity, while the high-velocity maser features show accelerations that are consistent with zero. We have also used the High-Sensitivity Array to make a high-sensitivity very long baseline interferometric map of the maser system in CGCG 074-064, which reveals that the masers reside in a thin, edge-on disk with a diameter of ~1.5mas (0.6pc). Fitting a three-dimensional warped disk model to the data, we measure a black hole mass of 2.42_-0.20_^+0.22^x10^7^M_{sun}_ and a geometric distance to the system of 87.6_-7.2_^+7.9^Mpc. Assuming a cosmic microwave background-frame recession velocity of 7308+/-150km/s, we constrain the Hubble constant to H_0_=81.0_-6.9_^+7.4^(stat.)+/-1.4(sys.)km/s/Mpc.