NASA is currently carrying out science and technical studies to identify its next astronomy flagship mission, slated to begin development in the 2020s. It has become clear that a Large Ultraviolet/Optical/IR (LUVOIR) surveyor mission (dprimary≈12 m, Δλ≈1000 Å, 2 μm spectroscopic bandpass) can carry out the largest number of NASA’s exoplanet and astrophysics science goals over the coming decades. The science grasp of an LUVOIR surveyor is broad, ranging from the direct detection of potential biomarkers on rocky planets to the flow of matter into and out of galaxies and the history of star-formation across cosmic time. There are technical challenges for several aspects of the LUVOIR surveyor concept, including component level technology readiness maturation and science instrument concepts for a broadly capable ultraviolet spectrograph. We present the scientific motivation for, and a preliminary design of, a multiplexed ultraviolet spectrograph to support both the exoplanet and astrophysics goals of the LUVOIR surveyor mission concept, the combined high-resolution and imaging spectrograph for the LUVOIR surveyor (CHISL). CHISL includes a high-resolution (R≈120,000; 1000 to 1700 Å) point-source spectroscopy channel and a medium-resolution (R≥14,000 from 1000 to 2000 Å in a single observation and R∼24,000 to 35,000 in multiple grating settings) imaging spectroscopy channel. CHISL addresses topics ranging from characterizing the composition and structure of planet-forming disks to the feedback of matter between galaxies and the intergalactic medium. We present the CHISL concept, a small sample of representative science cases, and the primary technological hurdles. Technical challenges include high-efficiency ultraviolet coatings and high-quantum efficiency, large-format, photon counting detectors. We are actively engaged in laboratory and flight characterization efforts for all of these enabling technologies as components on sounding rocket payloads under development at the University of Colorado. We describe two payloads that are designed to be pathfinder instruments for the high-resolution (CHESS) and imaging spectroscopy (SISTINE) arms of CHISL. We are carrying out this instrument design, characterization, and flight-testing today to support the new start of an LUVOIR surveyor mission in the next decade.