We propose two distinct atom interferometer gravitational wave detectors, one terrestrial and another satellite-based, utilizing the core technology of the Stanford 10 m atom interferometer presently under construction. Each configuration compares two widely separated atom interferometers run using common lasers. The signal scales with the distance between the interferometers, which can be large since only the light travels over this distance, not the atoms. The terrestrial experiment with baseline ~1 km can operate with strain sensitivity ~10^(-19) / Hz^(1/2) in the 1 Hz - 10 Hz band, inaccessible to LIGO, and can detect gravitational waves from solar mass binaries out to megaparsec distances. The satellite experiment with baseline ~1000 km can probe the same frequency spectrum as LISA with comparable strain sensitivity ~10^(-20) / Hz^(1/2). The use of ballistic atoms (instead of mirrors) as inertial test masses improves systematics coming from vibrations, acceleration noise, and significantly reduces spacecraft control requirements.