We present new X-ray, radio, and optical observations of the unidentified X-ray source 1E 1207.4 - 5209, which lies at the center of the shell-like supernova remnant G296.5 + 10.0. On the basis of its high X-ray to optical flux ratio, it had already been suggested that this source is an isolated neutron star associated with the supernova remnant. This is strongly supported by new ROSAT data, which are well fitted with a blackbody spectrum with T similar to 3 x 10(6) K, consistent with emission from a relatively young neutron star (similar to 10(4) yr) at the supernova remnant distance of about 1.5 kpc. If confirmed, this would be the second pulsar (after Geminga) not detected at radio wavelengths. Other possible interpretations, involving peculiar low-mass X-ray binaries, are discussed. The alternate possibility that 1E 1207.4-5209 is aBL Lac object is ruled out by a new upper limit of similar to 0.1 mJy at 6 cm.