Entanglement swapping allows to establish entanglement between independent particles that never interacted nor share any common past. This feature makes it an integral constituent of quantum repeaters. Here, we demonstrate entanglement swapping with time-synchronized independent sources with a fidelity high enough to violate a Clauser-Horne-Shimony-Holt inequality by more than four standard deviations. The fact that both entangled pairs are created by fully independent, only electronically connected sources ensures that this technique is suitable for future long-distance quantum communication experiments as well as for novel tests on the foundations of quantum physics.To take full advantage of the powerful features of quantum information processing schemes [1], large scale quantum networks will have to be realized. These will inevitably involve the reliable distribution of entanglement [2] between distant, independent nodes. Photons are well suited to cover these distances as they do not tend to interact with the environment and can easily be transmitted via fibers or optical free-space links. Today, these methods are limited to distances on the order of a hundred kilometers [4, 5? ] due to photon loss and detector noise [6]. Quantum repeaters [7,8,9,10], which repeatedly swap and distill entanglement along a chain of distant sources, are expected to overcome this limitation.The three principal ingredients of quantum repeaters are quantum memories [9,10], entanglement distillation [11,12], and entanglement swapping [13]. While a real-world implementation of a quantum repeater is still far down the road, gradual progress has been achieved in realizing its constituents [14, 16, 17, 18, 19, 20, 21, 22? ]. In particular any future realization of a quantum repeater will involve entanglement swapping with pairs emitted from distant, independent sources.Recently, the independence of the sources used for entanglement swapping was shown to be not only of practical interest. In [23] it is argued that independence in such an experiment allows to place even tighter restrictions on local hidden variable theories [24] than in experiments on pairs emitted directly by one source. This allows to circumvent the loophole of inefficient detectors. Therefore, the use of independent sources for entanglement swapping could help to close all loop holes, which up to now had to be closed in separate experiments [22,25,26,27] [22]. In all of these experiments a crucial requirement for use in quantum repeaters remains unfulfilled: the sources must be separable by large distances. In [14, 18, 20, 22? ] the entangled pairs were created by interaction of one optical pump with one or two nonlinear media, while in [28] the two laser beams pumping two separate nonlinear media were not optically independent. To separate the sources in any of these implementations would require to distribute intense pump beams over large distances. That goal is practically unfeasible given dispersion, high loss at the pump wavelengths and path length fluctuation...