  We theoretically show that the spin Hall effect arises in a Bose-Einstein
condensate (BEC) of neutral atoms interacting via the magnetic dipole-dipole
interactions (MDDIs). Since the MDDI couples the total spin angular momentum
and the relative orbital angular momentum of two colliding atoms, it works as a
spin-orbit coupling. Thus, when we prepare a BEC in a magnetic sublevel $m=0$,
thermally and quantum-mechanically excited atoms in the $m=1$ and $-1$ states
feel the Lorentz-like foces in the opposite directions. This is the origin for
the emergence of the the spin Hall effect. We define the mass-current and
spin-current operators from the equations of continuity and calculate the spin
Hall conductivity from the off-diagonal current-current correlation function
within the Bogoliubov approximation. We find that the correction of the current
operators due to the MDDI significantly contributes to the spin Hall
conductivity. Possible experimental situation is also discussed.
