We have studied the duration distribution of the gamma-ray bursts of the first BATSE catalog. We find a bimodality in the distribution, which separates GRBs into two classes: short events (less than 2 s) and longer ones (more than 2 s). Both sets are distributed isotropically and inhomogeneously in the sky. We find that their durations are anticorrelated with their spectral hardness ratios: short GRBs are predominantly harder, and longer ones tend to be softer. Our results provide a first GRB classification scheme based on a combination of the GRB temporal and spectral properties.