We create independent, synchronized single-photon sources with built-in quantum memory based on two remote cold atomic ensembles. The synchronized single photons are used to demonstrate efficient generation of entanglement. The resulting entangled photon pairs violate a Bells Inequality by 5 standard deviations. Our synchronized single photons with their long coherence time of 25 ns and the efficient creation of entanglement serve as an ideal building block for scalable linear optical quantum information processing.