We present the result of astrometric observations of the radio pulsar PSR B0656+14, made using the Very Long Baseline Array. The parallax of the pulsar is pi = 3.47 +/- 0.36 milliarcsec, yielding a distance 288(-27)(+33) pc. This independent distance estimate has been used to constrain existing models of thermal X-ray emission from the neutron star's photosphere. Simple blackbody fits to the X-ray data formally yield a neutron star radius R-infinity similar to 7-8.5 km. With more realistic fits to a magnetized hydrogen atmosphere, any radius between similar to13 and similar to20 km is allowed.