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The prospect of quantum networks, in which quantum information is carried by single photons in photonic circuits, has long been the driving force behind the effort to achieve all-optical routing of single photons. We realized a single-photon–activated switch capable of routing a photon from any of its two inputs to any of its two outputs. Our device is based on a single atom coupled to a fiber-coupled, chip-based microresonator. A single reflected control photon toggles the switch from high reflection (R ~ 65%) to high transmission (T ~ 90%), with an average of ~1.5 control photons per switching event (~3, including linear losses). No additional control fields are required. The control and target photons are both in-fiber and practically identical, making this scheme compatible with scalable architectures for quantum information processing.