We report a crossover from chaotic to self-organized critical dynamics in the Portevin-Le Chatelier effect in single crystals of Cu-10% Al in tension as a function of the applied strain rate. For low and intermediate strain rates, we provide an unambiguous support for the existence of chaotic stress drops by showing the existence of a finite correlation dimension and a stable positive Lyapunov exponent. A surrogate data analysis rules out the possibility that the time series is due to a power law stochastic process. As the strain rate is increased, the distributions of stress drops and the time intervals between the stress drops change from peaked to power law type with an exponent close to unity reminiscent of self-organized critical state. A scaling relation compatible with self-organized criticality relates the various exponents. The absence of a finite correlation dimension and a stable positive Lyapunov exponent at the highest strain rate also supports the evidence of crossover.