Conclusions. The NGC 2006-SL 538 cluster pair shows radial velocities, stellar population and dynamical parameters consistent with a gravitational bound entity and, considering that the velocity dispersion of the stars in LMC is <= 20 km s(-1), we reject them as a chance alignment. We conclude that this is a genuine binary cluster pair, and we propose that their differences in ages and stellar population chemistry is most likely due to variances in their chemical enrichment history within their environment. We suggest that they may have formed in a loosely bound star-formation complex which saw initial fragmentation but then had its clusters become a gravitationally bound pair by tidal capture.