We investigate the solar wind as a source for the deposits of hydrogen at the lunar poles. We create a Monte Carlo model that simulates the migration of atmospheric particles through the lunar exosphere. Making the model general enough to incorporate any physical process that might affect the particles, we develop a tool that estimates the number and form of particles that reach and stick to lunar cold traps. Each particle is allowed to follow a series of ballistic trajectories as it hops around the surface of the Moon. We trace the path of the particle until it is removed from the system by photo-processes such as ionization or dissociation, by thermal escape, or by reaching a cold trap. Accumulating statistics on the outcomes for various input particles, we determine the amount and form of hydrogen able to migrate to the lunar cold traps over time for a typical solar wind input flux. We find that although the fraction of hydrogen delivered to the Moon that ultimately reaches the poles is small, a slow steady source like the solar wind has provided enough hydrogen over 83 Myr to account for the observed deposits. Also, we find that an enrichment in the ratio occurs by the migration process. The amount of fractionation is dependent on the molecular form of the migrating hydrogen. Atomic deuterium/hydrogen is enriched by a factor of 4 over the delivered fraction by the migration process. ¿ 2000 American Geophysical Union