  An experiment in Low Earth Orbit (LEO) is proposed to measure components of
the Riemann curvature tensor using atom interferometry. We show that the
difference in the quantum phase $\Delta\phi$ of an atom that can travel along
two intersecting geodesics is given by $mR_{0i0j}/\hbar$ times the spacetime
volume contained within the geodesics. Our expression for $\Delta\phi$ also
holds for gravitational waves in the long wavelength limit.
