For many chaotic systems, the stretching and the folding that generate the chaos also rapidly mix up the phase space. The rate at which this mixing occurs (the rate of decay of correlations) is a fundamental characteristic of the dynamics. It describes the speed at which mass in phase space approaches the equilibrium distribution, it indicates how quickly physical observables become decorrelated, and it tells the experimentalist how rapidly he can expect initial transient behaviour to disappear. We present a rigorous numerical method for (i) estimating the rate of decay, and (ii) finding those observables that become decorrelated at the slowest possible rate.