During orbital migration of a giant extrasolar planet via ejection of planetesimals (Murray et al.~1998), inner mean motion resonances can be strong enough to cause planetesimals to graze or impact the star. We integrate numerically the motions of particles which pass through the 3:1 or 4:1 mean motion resonances of a migrating Jupiter mass planet. We find that many particles can be trapped in the 3:1 or 4:1 resonances and pumped to high enough eccentricities that they impact the star. This implies that for a planet migrating a substantial fraction of its semi major axis, a significant fraction of its mass in planetesimals could impact the star. This process may be capable of enriching the metallicity of the star, and at a time when the star is no longer fully convective. Upon close approaches to the star the surfaces of these planetesimals will be sublimated. Orbital migration should cause continuing production of evaporating bodies, suggesting that this process should be detectable with searches for transient absorption lines in young stars. The remainder of the particles will not impact the star but can be subsequently ejected by the planet as it migrates further inwards. This allows the planet to migrate a substantial fraction of its initial semi-major axis via ejection of planetesimals.