The Cs2LiYCl6:Ce3+ (CLYC) scintillator is being widely employed in nuclear physics, planetary science, radiation environmental monitoring, nuclear security, and nonproliferation communities. The time resolution of a 1 × 1-in. CLYC scintillation detector is reported in this paper. It was measured by the use of a high sampling rate DRS4 waveform digitizer and an EJ-309 liquid scintillation detector. The digitizer was first characterized with regard to its intrinsic time resolution and then the time resolution of the EJ-309 detector was investigated. It served as a reference detector in the time resolution measurements for the CLYC detector. The time pick-off techniques used were the constant fraction discrimination and leading edge discrimination methods. In addition, the Savitzky-Golay filter was used to further improve the measured time resolutions. This filter was shown to be an effective approach to improving time resolution when the signal-to-noise ratio is low.