  The presence of ``Hot Jupiters'', Jovian mass planets with very short orbital
periods orbiting nearby main sequence stars, has been proposed to be primarily
due to the orbital migration of planets formed in orbits initially much further
from the parent star. The migration of giant planets would have profound
effects on the evolution of inner terrestrial planets in these systems, and
previous analyses have assumed that no terrestrial planets survive after
migration has occurred. We present numerical simulations showing that a
significant fraction of terrestrial planets could survive the migration
process, eventually returning to circular orbits relatively close to their
original positions. A fraction of the final orbits are in the Habitable Zone,
suggesting that planetary systems with close-in giant planets are viable
targets for searches for Earth-like habitable planets around other stars.
