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50 years ago, John Bell proved that no theory of nature that obeys locality and realism can reproduce all the predictions of quantum theory. Numerous Bell inequality tests have been reported, however, all experiments reported so far required additional assumptions to obtain a contradiction with local realism, resulting in loopholes. Here we will present a Bell experiment that is free of any such additional assumption. We use an event-ready scheme that enables the generation of robust entanglement between distant electron spins. Efficient spin read-out avoids the fair-sampling assumption, while the use of fast random-basis selection and spin read-out combined with a spatial separation of 1.3 km ensure the required locality conditions. We performed 245 trials that tested the CHSH-Bell inequality S<= 2 and found S= 2.42+-0.20. A null-hypothesis test yields a probability of P<= 0.039 that a local-realist model for space …