We report the discovery of a highly dispersed fast radio burst, FRB~181123, from an analysis of $sim$1500~hr of drift-scan survey data taken using the Five-hundred-meter Aperture Spherical radio Telescope (FAST). The pulse has three distinct emission components, which vary with frequency across our 1.0--1.5~GHz observing band. We measure the peak flux density to be $>0.065$~Jy and the corresponding fluence $>0.2$~Jy~ms. Based on the observed dispersion measure of 1812~cm$^{-3}$~pc, we infer a redshift of $sim 1.9$. From this, we estimate the peak luminosity and isotropic energy to be $lesssim 2times10^{43}$~erg~s$^{-1}$ and $lesssim 2times10^{40}$~erg, respectively. With only one FRB from the survey detected so far, our constraints on the event rate are limited. We derive a 95% confidence lower limit for the event rate of 900 FRBs per day for FRBs with fluences $>0.025$~Jy~ms. We performed follow-up observations of the source with FAST for four hours and have not found a repeated burst. We discuss the implications of this discovery for our understanding of the physical mechanisms of FRBs.