We have embedded an artificial atom, a superconducting transmon qubit, in an open transmission line and investigated the strong scattering of incident microwave photons (∼6  GHz). When an input coherent state, with an average photon number N≪1 is on resonance with the artificial atom, we observe extinction of up to 99.6% in the forward propagating field. We use two-tone spectroscopy to study scattering from excited states and we observe electromagnetically induced transparency (EIT). We then use EIT to make a single-photon router, where we can control to what output port an incoming signal is delivered. The maximum on-off ratio is around 99% with a rise and fall time on the order of nanoseconds, consistent with theoretical expectations. The router can easily be extended to have multiple output ports and it can be viewed as a rudimentary quantum node, an important step towards building quantum information networks.