  If dark matter has a non-zero self-interaction cross-section, then dark
matter halos of individual galaxies in cluster cores should experience a drag
force from the ambient dark matter of the cluster, which will not affect the
stellar components of galaxies, and thus will lead to a separation between the
stellar and dark matter. If the cross-section is only a few decades below its
current astrophysically determined upper limit, then kpc-scale separations
should result. However, such separations will be observable only under very
favorable conditions. Abell 3827 is a nearby late stage cluster merger with
four massive central ellipticals within 20 kpc of each other. The ten strong
lensing images tightly surrounding the ellipticals provide an excellent set of
constraints for a free-form lens reconstruction. Our free-form mass maps show a
massive dark extended clump, about 6 kpc from one of the ellipticals. The
robustness of this result has been tested with many reconstructions, and
confirmed with experiments using synthetic lens mass distributions. Interpreted
in terms of dark matter collisionality, our result yields sigma/m ~ 4.5 10^{-7}
(t/10^{10} yr)^{-2} cm^2/g, where t is the merger's age.
