Single-quantum emitters emit only one photon at a time(1,2), but the properties of the photon depend on how the emitter is excited(3). Incoherent excitation is simple and broadly used with solid-state emitters such as quantum dots, but does not allow direct manipulation of the quantum state. Coherent, resonant excitation on the other hand is used in pump-probe techniques to examine the quantum state of the emitter(4), but does not permit collection of the single-photon emission. Coherent control with simultaneous generation of photons has been an elusive goal in solid-state approaches, where, because of strong laser scattering at the detection wavelength, measurement of resonant emission has been limited to cross-polarized detection(5) or Stokes-shift techniques(6,7). Here we demonstrate that a semiconductor quantum dot in a microcavity can be resonantly driven and its single-photon emission extracted background free. Under strong continuous-wave excitation, the dot undergoes several Rabi oscillations before emitting, which are visible as oscillations in the second-order correlation function. The quantum-dot states are therefore dressed , resulting in a Mollow-triplet emission spectrum. Such coherent control will be necessary for future high-efficiency sources of indistinguishable single photons(3,8), which can be used for quantum key distribution(9) or through post-selection(10) to generate entangled photon pairs(11,12).