Recent measurement indicate the enriched production of He3 but not of H2 in some solar flares. This leads to an apparent paradox if the reaction H+He3→H2+He3 is the dominant mode of production. A detailed Monte Carlo calculation for this reaction is performed to determine the kinematical regions where He3 dominates. It is found that for the thin-target case, no such region exists. For the thick-target case, He3 dominates in the backward and perpendicular directions relative to the incident proton. Obtaining reliable production ratios above ~10 MeV/nucleon is not possible because of uncertainties in the production cross section at high incident proton energies (Ep?400 MeV). One possibility recently proposed by Ramaty and Kozlovsky (1974) is that the measured He3 are accelerated after being produced by protons impinging on the solar atmosphere. We examine this hypothesis and conclude that the required postproduction acceleration must occur over very small distances on a solar scale and before photospheric turbulence mixes the separated H2 and He3. It is concluded that a thick-target model based on primary protons mirroring just below the solar surface is the most likely source of the He3 enriched events.