LUX is a two-phase (liquid/gas) xenon time projection chamber designed to detect nuclear recoils from interactions with dark matter particles. Signals from the LUX detector are processed by custom-built analog electronics which provide properly shaped signals for the trigger and data acquisition (DAQ) systems. The DAQ is comprised of commercial digitizers with firmware customized for the LUX experiment. Data acquisition systems in rare-event searches must accommodate high rate and large dynamic range during precision calibrations involving radioactive sources, while also delivering low threshold for maximum sensitivity. The LUX DAQ meets these challenges using real-time baseline sup- pression that allows for a maximum event acquisition rate in excess of 1.5 kHz with virtually no deadtime. This paper describes the LUX DAQ and the novel acquisition techniques employed in the LUX experiment.