In free-space single-photon quantum key distribution (QKD), the error rate due to daytime background photons can be reduced with strong temporal filtering. In this case, the improvement in performance is determined by the receiver s ability to resolve signal-photon arrival times. We use fast clock recovery and commercially available single-photon detectors with timing resolution enhanced by additional electronic circuitry to implement temporal gating down to 50 ps in a free-space QKD system. The single-photon channel operates at 850 nm, and the improved timing resolution enables transmission rates of 1.25 GHz. We observe daytime quantum bit error rates of 0.04, which is less than one-third of the ungated error rate. We present the design and performance of the system and demonstrate its benefit to free-space QKD.