We present reverberation-mapping lags and black-hole mass measurements using the CIV 1549 broad emission line from a sample of 349 quasars monitored as a part of the Sloan Digital Sky Survey Reverberation Mapping Project. Our data span four years of spectroscopic and photometric monitoring for a total baseline of 1300 days. We report significant time delays between the continuum and the CIV 1549 emission line in 52 quasars, with an estimated false-positive detection rate of 10%. Our analysis of marginal lag measurements indicates that there are on the order of 100 additional lags that should be recoverable by adding more years of data from the program. We use our measurements to calculate black-hole masses and fit an updated CIV radius-luminosity relationship. Our results significantly increase the sample of quasars with CIV RM results, with the quasars spanning two orders of magnitude in luminosity toward the high-luminosity end of the CIV radius-luminosity relation. In addition, these quasars are located at among the highest redshifts (z~1.4-2.8) of quasars with black hole masses measured with reverberation mapping. This work constitutes the first large sample of CIV reverberation-mapping measurements in more than a dozen quasars, demonstrating the utility of multi-object reverberation mapping campaigns.