The observation of quantum-dot resonance fluorescence enabled a new solid-state approach to generating single photons with a bandwidth approaching the natural linewidth of a quantum-dot transition. Here, we operate in the small Rabi frequency limit of resonance fluorescence--the Heitler regime--to generate subnatural linewidth and high-coherence quantum light from a single quantum dot. The measured single-photon coherence is 30 times longer than the lifetime of the quantum-dot transition, and the single photons exhibit a linewidth which is inherited from the excitation laser. In contrast, intensity-correlation measurements reveal that this photon source maintains a high degree of antibunching behavior on the order of the transition lifetime with vanishing two-photon scattering probability. Generating decoherence-free phase-locked single photons from multiple quantum systems will be feasible with our approach.