We report the demonstration of strong coupling between single Cesium atoms and a high-Q chip-based microresonator. Our toroidal microresonators are compact, Si chip-based whispering gallery mode resonators that confine light to small volumes with extremely low losses, and are manufactured in large numbers by standard lithographic techniques. Combined with the capability to couple efficiently light to and from these microresonators by a tapered optical fiber, toroidal microresonators offer a promising avenue towards scalable quantum networks. Experimentally, laser cooled Cs atoms are dropped onto a toroidal microresonator while a probe beam is critically coupled to the cavity mode. When an atom interacts with the cavity, it modifies the resonance spectrum of the cavity, leading to rejection of some of the probe light from the cavity, and thus to an increase in the output power. By observing such transit events while systematically detuning the cavity from the atomic resonance, we determine the maximal accessible single-photon Rabi frequency of Ω0/2π (100 ± 24) MHz. This value puts our system in the regime of strong coupling, being significantly larger than the dissipation rates in our system.