We introduce a protocol through which a pair of quantum mechanical devices may be used to generate n random bits that are ε-close in statistical distance from n uniformly distributed bits, starting from a seed of O(log n log 1/ε) uniform bits. The bits generated are certifiably random, based only on a simple statistical test that can be performed by the user, and on the assumption that the devices obey the no-signalling principle. No other assumptions are placed on the devices' inner workings: it is not necessary to even assume the validity of quantum mechanics. This journal is © 2012 The Royal Society.