We have studied the deflection of ground-state sodium atoms passing through a micron-sized parallel-plate cavity by measuring the intensity of a sodium atomic beam transmitted through the cavity as a function of cavity plate separation. This experiment provides clear evidence for the existence of the Casimir-Polder force, which is due to modification of the ground-state Lamb shift in the confined space of a cavity. Our results confirm the magnitude of the force and the distance dependence predicted by quantum electrodynamics.