The accelerated expansion of the universe motivates a wide class of scalar field theories that modify General Relativity (GR) on large scales. Such theories require a screening mechanism to suppress the new force in regions where the weak field limit of GR has been experimentally tested. We have used atom interferometry to measure the acceleration of an atom toward a macroscopic test mass inside a high vacuum chamber, where new forces can be unscreened. Our measurement shows no evidence of new forces, a result that places stringent bounds on chameleon and symmetron theories of modified gravity