  We report on a discovery of a promising candidate as a black widow
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) hours using the Bohyunsan 1.8-m Telescope, Lulin One-meter
Telescope, Canada-France-Hawaii Telescope, and Gemini-North. At the optical
position, an X-ray source was marginally detected in the Swift/XRT 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 =
1.6+/-0.7 and F(0.3-7keV) = 3.5e-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 black widow 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 black widow millisecond pulsar binary that showed an
orbitally-modulated emission in X-rays.
