We report on the discovery of a promising candidate for a black widow (BW) millisecond pulsar binary, 4FGL J0336.0+7502, which shows many pulsar-like properties in the 4FGL-DR2 catalog. Within the 95% error region of the LAT source, we identified an optical counterpart with a clear periodicity at P_orb_=3.718178(9)hr using the Bohyunsan 1.8m Telescope, the Lulin One-meter Telescope, the Canada-France-Hawaii Telescope, and Gemini-North. At the optical position, an X-ray source was marginally detected in the Swift/X-Ray Telescope archival data, and the detection was confirmed by our Chandra/ACIS DDT observation. The spectrum of the X-ray source can be described by a power- law model of {Gamma}_x_=1.6+/-0.7 and F_0.3-7keV_=3.5_-1.0_^+1.2^x10^-14^erg/cm^2^/s. The X-ray photon index and the low X-ray-to-{gamma}-ray flux ratio (i.e., <1%) are both consistent with that of many known BW pulsars. There is also a hint of an X-ray orbital modulation in the Chandra data, although the significance is very low (1.3{sigma}). If the pulsar identity and the X-ray modulation are confirmed, it would be the fifth BW millisecond pulsar binary that showed an orbitally modulated emission in X-rays.