Quantum memory networks as an intermediate stage in the development of a quantum internet1 will enable a number of significant applications2-5. To connect and entangle remote quantum memories, it is best to use photons. In previous experiments6-13, entanglement of two memory nodes has been achieved via photon interference. Going beyond the state of the art by entangling many quantum nodes at a distance is highly sought after. Here, we report the entanglement of three remote quantum memories via three-photon interference. We employ laser-cooled atomic ensembles and make use of a ring cavity to enhance the overall efficiency of our memory–photon entanglement. By interfering three single photons from three separate set-ups, we create entanglement of three memories and three photons. Then, by measuring the photons and applying feed-forward, we achieve heralded entanglement between the three memories. Our experiment may be employed as a building block to construct larger and complex quantum networks14,15.The entanglement of three remote quantum memories based on 87Rb atoms is created via three-photon interference by enhancing the memory–photon entanglement in ring cavities, demonstrating a genuine quantum network involving more than two quantum nodes.