A model He exosphere of Mercury is developed whose source derives from accretion of the small fraction of solar wind He++ that is captured by the magnetosphere and absorbed at the planetary surface. The model is based on a lunar analogy whereby the surface is saturaged in He. Surface and radial density distributions are derived, and the day side concentration is determined by requiring the limb intensity at 584 ¿ to equal the observed intensity. To maintain the He exosphere, we find that only the fraction 6.2¿10-4 of the solar wind He++ flux intercepted by the magnetosphere need be captured. This corresponds to a total accretion rate of 6.8¿1022 He++ s-1 at the surface, which also represents the upper limit to the total outgassing rate of He from the interior.