  In the standard model, we study CP violating rate asymmetries in the decay
b->d l^+ l^- when one of the leptons is polarised. We find an asymmetry of (5
-- 15)% in the polarised decay spectrum which is comparable to known results
for the unpolarised case. In the kinematic region separating the rho-omega and
$c \bar c$ resonances, which is also theoretically cleanest, the polarised
contribution to the asymmetry is larger than the unpolarised results. In order
to observe a 3 sigma signal for direct CP violation in the polarised spectrum,
assuming 100% efficiency, about 10^10 $B \bar B$ pairs are required at a B
factory. Our results indicate an asymmetric contribution from the individual
polarisation states to the unpolarised CP asymmetry. Taking advantage of this,
one can attribute any new physics to be most sensitive to a specific
polarisation state.
