The motion of individual cesium atoms trapped inside an optical resonator is revealed with the atom-cavity microscope (ACM), A single atom moving within the resonator generates Large variations in the transmission of a weak probe Laser, which are recorded in real time. An inversion algorithm then allows individual atom trajectories to be reconstructed from the record of cavity transmission and reveals single atoms bound in orbit by the mechanical forces associated with single photons. In these initial experiments, the ACM yields 2-micrometer spatial resolution in a 10-microsecond time interval. Over the duration of the observation, the sensitivity is near the standard quantum limit for sensing the motion of a cesium atom.