Quantum repeaters will be critical to quantum communication and quantum computation. Here, we describe a mechanism that permits the creation of entanglement between two qubits, connected by fibre, with probability arbitrarily close to one and in constant time. We show how this mechanism may be extended to ensure that the entanglement has high fidelity without compromising these properties. Finally, we describe how it may be used to construct a quantum repeater that is capable of creating a linear quantum network connecting two distant qubits with high fidelity. The communication rate is shown to be a function of the maximum distance between any two adjacent quantum repeaters rather than of the entire length of the network.