RESUMEN
An experimental test of Bell's inequality allows ruling out any local-realistic description of nature by measuring correlations between distant systems. While such tests are conceptually simple, there are strict requirements concerning the detection efficiency of the involved measurements, as well as the enforcement of spacelike separation between the measurement events. Only very recently could both loopholes be closed simultaneously. Here we present a statistically significant, event-ready Bell test based on combining heralded entanglement of atoms separated by 398 m with fast and efficient measurements of the atomic spin states closing essential loopholes. We obtain a violation with S=2.221±0.033 (compared to the maximal value of 2 achievable with models based on local hidden variables) which allows us to refute the hypothesis of local realism with a significance level P<2.57×10^{-9}.