We report the detection of sub-Saturn-mass planet MOA-2008-BLG-310Lb and argue that it is the strongest candidate yet for a bulge planet. Deviations from the single-lens fit are smoothed out by finite-source effects and so are not immediately apparent from the light curve. Nevertheless, we find that a model in which the primary has a planetary companion is favored over the single-lens model by Deltachi^2 ~ 880 for an additional three degrees of freedom. Detailed analysis yields a planet/star mass ratio q=(3.3+/-0.3)x10^{-4} and an angular separation between the planet and star within 10% of the angular Einstein radius. The small angular Einstein radius, theta_E=0.155+/-0.011 mas, constrains the distance to the lens to be D_L>6.0 kpc if it is a star (M_L>0.08 M_sun). This is the only microlensing exoplanet host discovered so far that must be in the bulge if it is a star. By analyzing VLT NACO adaptive optics images taken near the baseline of the event, we detect additional blended light that is aligned to within 130 mas of the lensed source. This light is plausibly from the lens, but could also be due to a companion to lens or source, or possibly an unassociated star. If the blended light is indeed due to the lens, we can estimate the mass of the lens, M_L=0.67+/-0.14 M_sun, planet mass m=74+/-17 M_Earth, and projected separation between the planet and host, 1.25+/-0.10 AU, putting it right on the snow line. If not, then the planet has lower mass, is closer to its host and is colder. To distinguish among these possibilities on reasonable timescales would require obtaining Hubble Space Telescope images almost immediately, before the source-lens relative motion of mu=5 mas yr^{-1} causes them to separate substantially.
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