This chapter introduces the celebrated random choice method, which has provided the earliest, but still very effective, scheme for constructing globally defined, admissible BV solutions to the Cauchy problem for strictly hyperbolic systems of conservation laws, under initial data with small total variation. The solution is obtained as the limit of a sequence of approximate solutions, which are constructed by patching together solutions to Riemann problems and thus are composed of constant states, shocks and rarefaction waves.