Relative proper motions, based on 108 orbits of Hubble Space Telescope Fine Guidance Sensor data extending from 1992 to 2006, are reported for 74 stars in the open cluster M35 (NGC 2168). A subset of 22 of these objects are then used to compute the cluster's internal proper motion dispersions in both right ascension and declination. We find that these dispersions are equal to within their measurement errors. The average one-dimensional dispersion is 0.018 ± 0.002 arcsec century-1. When combined with the M35 radial velocity dispersion of 0.65 ± 0.10 km s-1 found by Geller et al., this produces a cluster distance of 762 ± 145 pc. Using isochrone fits to the cluster main sequence, this distance suggests that M35 has an age of about 133 Myr. Although this age is consistent with that typically found for M35, the formal error in the dynamical distance of ±19% can accommodate ages between 65 Myr and 201 Myr.