A new scheme for generating good pseudo-random numbers, based on the composition of chaotic maps, is studied. In this method, hereafter called the chaotic stream cipher, one first uses a known chaotic dynamical system to generate a sequence of pseudo-random bytes, then applies certain permutations to them, using the discretized version of another two-dimensional chaotic map. Standard statistical tests of this scheme, as well as other known chaos-based random number generators, are performed and compared. We show that this new scheme can generate a high percentage of usable pseudo-random numbers, while maintaining a large enough key space for potential use in encryptions.