  Characterizing many-body systems through the quantum correlations between
their constituent particles is a major goal of quantum physics. Although
entanglement is routinely observed in many systems, we report here the
detection of stronger correlations - Bell correlations - between the spins of
about 480 atoms in a Bose-Einstein condensate. We derive a Bell correlation
witness from a many-particle Bell inequality involving only one- and two-body
correlation functions. Our measurement on a spin-squeezed state exceeds the
threshold for Bell correlations by 3.8 standard deviations. Our work shows that
the strongest possible non-classical correlations are experimentally accessible
in many-body systems, and that they can be revealed by collective measurements.
