  We propose and analyze a protocol for observing a violation of the
Clauser-Horne-Shimony-Holt (CHSH) Bell inequality using two spatially separated
Bose-Einstein condensates (BECs). To prepare the Bell-correlated state,
spin-changing collisions are used to first prepare a two-mode squeezed BEC.
This is then split into two BECs by controlling the spatial wavefunction,
$\textit{e.g.}$ by modifying the trapping potential. Finally, spin-changing
collisions are also exploited locally, to compensate local squeezing terms. The
correlators appearing in the inequality are evaluated using three different
approaches. In the first approach, correlators are estimated using normalized
expectation values of number operators, in a similar way to evaluating
continuous-variable Bell inequalities. An improvement to this approach is
developed using the sign-binning of total spin measurements, which allows for
the construction of two-outcome measurements and violations of the CHSH
inequality without auxiliary assumptions. Finally, we show a third approach
where maximal violations of the CH inequality can be obtained by assigning zero
values to local vacua outcomes under a no-enhancement assumption. The effect of
loss and imperfect detection efficiency is investigated and the observed
violations are found to be robust to noise.
