The identification of randomness and nonrandomness is a perennial problem in evolutionary research. Stochastic thinking in evolutionary biology and paleobiology has solidified the use of a statistical notion of chance, but the idea of chance in evolutionary studies goes beyond statistics. A duality arises from the use of a statistical meaning on the one hand, and a more strictly evolutionary meaning on the other. The former implies a combination of indiscriminate sampling and unpredictability due to multiple causes; the latter codifies independence from adaptation and the directionality imposed by natural selection. Often these meanings are kept separate in evolutionary research, used in isolation according to the empirical situation or the goal of the investigator (recognition of pattern versus process). I argue that evolutionary studies in general and paleobiological studies in particular can benefit from the simultaneous application of statistical and evolutionary notions of chance. Following some background on the notion of chance and its use, I discuss a series of examples in which insight can be gained by explicit consideration of both meanings. Thus, typologies of extinction become clearer when phenomena like wanton extinction are made explicit; exaptive radiations are exposed as an alternative to adaptive radiations; the possible non-adaptive nature of deterministic chaos becomes sensible; the nonrandomness of community-assembly is put into question; parallel taxonomies of sorting rooted in different notions of nonrandomness are suggested as a means of facilitating understanding of relationships across the hierarchy; developmental constraints and self-organization are more easily distinguished from selective constraints; and a new term, "incidentals," is suggested to refer to both exaptations and nonaptations. Finally, I point to ways in which the dichotomy between chance and necessity can be approached in evolutionary theory, by showing that the dual nature of chance in evolution entails a distinction between functional and structural necessity, and that chance ultimately becomes a unifying concept for a number of criticisms to neo-Darwinism.