We report the identification of a very metal-poor damped Lyman-alpha system (DLA) at z_abs = 3.067295 that is modestly carbon-enhanced, with an iron abundance of ~1/700 solar ([Fe/H] = -2.84) and [C,O/Fe] ~ +0.6. Such an abundance pattern is likely to be the result of nucleosynthesis by massive stars. On the basis of 17 metal absorption lines, we derive a 2 sigma upper limit on the DLAs kinetic temperature of T_DLA <= 4700 K, which is broadly consistent with the range of spin temperature estimates for DLAs at this redshift and metallicity. While the best-fitting abundance pattern shows the expected hallmarks of Population III nucleosynthesis, models of high-mass Population II stars can match the abundance pattern almost as well. We discuss current limitations in distinguishing between these two scenarios and the marked improvement in identifying the remnants of Population III stars expected from the forthcoming generation of 30-metre class telescopes.