The first hydrostatic core (FHSC) represents a very early phase in the low-mass star Formation process, after collapse of the parent core has begun but before a true protostar has formed. This large (few AU), cool (100 K), pressure-supported core of molecular hydrogen is expected from theory, but has yet to be observationally verified. Here, we present observations of an excellent candidate for the FHSC phase: Per-Bolo 58, a dense core in Perseus that was previously believed to be starless. The 70 mu m flux of 65 mJy, from new deep Spitzer MIPS observations, is consistent with that expected for the FHSC. A low signal-to-noise detection at 24 mu m leaves open the possibility that Per-Bolo 58 could be a very low luminosity protostar, however....