We report evidence for a bimodality in damped Lyα systems (DLAs). Using [C II] 158 μm cooling rates, lc, we find a distribution with peaks at lc = 10−27.4 and 10−26.6 ergs s−1 H−1 separated by a trough at lcritc ≈ 10−27.0 ergs s−1 H−1. We divide the sample into DLAs with lc ≤ lcritc and DLAs with lc > lcritc and find the K-S probabilities that velocity width, metallicity, dust-to-gas ratio, and Si II equivalent width in the two subsamples are drawn from the same parent population are small. These quantities are significantly larger in the high cool population, while the H I column densities are indistinguishable in the two populations. We find the DLA gas is heated by local radiation fields and background radiation, rather than background radiation alone. The rare appearance of faint, extended objects in the Hubble Ultra Deep Field rules out in situ star formation as the dominant star-formation mode for the high cool population, but is compatible with in situ star formation as the dominant mode for the low cool population. Star formation in the high cool DLAs likely arises in Lyman break galaxies. Using Si II equivalent width as a mass indicator, we construct bivariate distributions of metallicity, lc, and areal SFR versus the mass indicators. Tentative evidence is found for correlations and parallel sequences, which suggest similarities with the bimodality found in nearby galaxies. We suggest that the transition-mass model provides a plausible scenario for the bimodality we have found. As a result, the bimodality in current galaxies may have originated in DLAs.