The isolated neutron star RX J185635-3754 is the closest known neutron star to the Sun. Based on HST WFPC2 obervations over a 3 year baseline, I report its proper motion (332 +/- 1 mas/yr at a position angle of 100.3 +/- 0.1 degrees) and parallax (16.5 +/- 2.3 mas; 61 pc). This proper motion brings the neutron star from the general vicinity of the Sco-Cen OB association. For an assumed neutron star radial velocity between -55 and -60 km/s, the runaway O star zeta Oph, the Upper Sco OB association, and the neutron star come into spatial coincidence between 0.9 and 1.0 million years ago. RX J185635-3754 may be the remnant of the original primary of the zeta Oph system. If so, the space velocity suggests that the neutron star received a kick of about 200 km/s at birth.