We report the discovery of a young planetary-mass brown dwarf in the ρ Oph cloud core. The object was identified as such with the aid of a 1.5-2.4 μm low-resolution spectrum obtained using the NIRC instrument on the Keck I telescope. Based on the COND model, the observed spectrum is consistent with a reddened (A_V ~ 15-16) brown dwarf whose effective temperature is in the range 1200-1800 K. For an assumed age of 1 Myr, comparison with isochrones further constrains the temperature to ~1400 K and suggests a mass of ~2-3 Jupiter masses. The inferred temperature is suggestive of an early T spectral type, which is supported by spectral morphology consistent with weak methane absorption. Based on its inferred distance (~100 pc) and the presence of overlying visual absorption, it is very likely to be a ρ Oph cluster member. In addition, given the estimated spectral type, it may be the youngest and least massive T dwarf found so far. Its existence suggests that the initial mass function for the ρ Oph star-forming region extends well into the planetary-mass regime.