The origin of stable self-replicating molecules represents a fundamental obstacle to the origin of life. The low fidelity of primordial replicators places restrictions on the quantity of information encoded in a primitive nucleic acid alphabet. Further difficulties for the origin of life are the role of drift in small primordial populations, reducing the rate of fixation of superior replicators, and the hostile conditions increasing random variation in fitness. Thus mutation, noise and drift are three independent stochastic effects that are assumed to make the evolution of life improbable. Here we show how noise present in hostile early environments, can increase the probability of faithful replication by amplifying selection in finite populations. Hence factors formerly considered inimical to the origin of life - environmental noise and drift in small populations - can give rise to conditions favorable to robust replication.