  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 $398\,\mathrm{m}$ with
fast and efficient measurements of the atomic spin states closing essential
loopholes. We obtain a violation with $S=2.221\pm0.033$ (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 $P<2.57\cdot10^{-9}$.
