If dark matter has a non-zero self-interaction cross-section, then dark matter haloes 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 favourable conditions. Abell 3827 is a nearby late stage cluster merger with four massive central ellipticals within 20 kpc of each other. The 10 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 σ/m≳ 4.5 10-7 (t/1010 yr)-2 cm2 g-1, where t is the merger’s age.