Frequency-dependent selection is an important determinant of the evolution of gametophytic self-incompatibility systems in plants, aposematic (warning) and cryptic coloration, systems of mimicry, competitive interactions among members of a population, mating preferences, predator-prey and host-parasite interactions, aggression and other behavioral traits. Previous theoretical studies of frequency-dependent selection have shown it to be a plausible mechanism for maintenance of genetic variability in natural populations. Here, through an analysis of a simple deterministic model for frequency-dependent selection, we demonstrate that complex dynamic behavior is possible under a broad range of parameter values. In particular, we show that the model exhibits not only cycles and chaos, but also, for a more restricted set of parameters, transient chaos and intermittency - alterations between an apparently deterministic behavior and apparently chaotic fluctuations. This behavior, which has not been stressed within the population genetics literature, provides an explanation for erratic dynamics of gene frequencies.