We demonstrate a quantum random number generator based on the random nature of the phase difference between two independent laser sources. The speed of random bit generation is determined by the photodetector bandwidth and the linewidth of the lasers used. The system implemented is robust and generates a probability distribution of quantum origin which is intrinsically uniform and thus in principle needs no randomness extraction. The phase is measured with telecom equipment routinely used for high capacity coherent optical communications, which allows to keep track of the phase drift of the lasers and is readily available in the telecommunication industry.