Close-in giant planets (e.g., "hot Jupiters") are thought to form far from their host stars and migrate inward, through the terrestrial planet zone, via torques with a massive gaseous disk. Here we simulate terrestrial planet growth during and after giant planet migration. Several-Earth-mass planets also form interior to the migrating jovian planet, analogous to recently discovered "hot Earths." Very-water-rich, Earth-mass planets form from surviving material outside the giant planet's orbit, often in the habitable zone and with low orbital eccentricities. More than a third of the known systems of giant planets may harbor Earth-like planets.