We have observed the prototypical dwarf nova U Gem at quiescence with the Chandra medium- and high-resolution gratings to accomplish the first study of resolved X-ray emission lines in a disk-accreting cataclysmic variable. Doppler tomograms constructed from optical spectra obtained close in time to the X-ray observation show a typical quiescent disk structure with an irradiated secondary but no prominent disk hot spot. The unprecedented spectral resolution of Chandra over past X-ray telescopes reveals prominent narrow emission lines of O, Ne, Mg, Si, S, and Fe. The line fluxes, ratios, and widths indicate that X-ray emission arises from a range of temperatures in a high-density (greater than 1014 cm-3) gas, moving at low (less than 300 km s-1) velocity, with a small (less than 107 cm) scale height compared to the white dwarf radius. Simple models with cooling flows, cooling flows plus isothermal zones, and thermal conduction give reasonable agreement with the low-temperature emission lines, but a good fit to the entire range of lines will require a better understanding of all the parameters that affect the boundary layer.