The assumption that classical conditioning depends on a contingent relation between the conditioned stimulus (CS) and the unconditioned stimulus (US), which was proposed some decades ago as an alternative to the traditional contiguity assumption, still is widely accepted as an empirical generalization, if no longer as a theoretical postulate. The first support for the contingency assumption was provided by experiments in which occasional CS-US pairings produced no response to the CS in random training--i.e., training in which the probability of the US was the same in the presence and absence of the CS. Those early experiments, the results of which too often are taken at face value, are reconsidered along with various later experiments that show conditioning, both of the CS and its context, in random training. The evidence suggests that CS-US contingency is neither necessary nor sufficient for conditioning and that the concept has long outlived any usefulness it may once have had in the analysis of conditioning.