Context : The LMC is known to be the host of a rich variety of star clusters of all ages .
A large number of them is seen in close projected proximity .
Ages have been derived for few of them showing differences up to few million years , hinting at being binary star clusters .
However , final confirmation needs to be done through spectroscopy measurements and dynamical analysis .

Aims : In the present work we focus on one of these LMC cluster pairs ( NGC 2006 - SL 538 ) and aim to determine whether the star cluster pair is a bound entity and , therefore , a binary star cluster or a chance alignment .

Methods : Using the MIKE echelle high-resolution spectrograph on the 6.5-meter Magellan-II Clay telescope at Las Campanas Observatory we have acquired integrated-light spectra of the two clusters , measuring their radial velocities with individual absorption features and cross-correlation of each spectrum with a stellar spectral library .

Results : We have measured radial velocities by two methods : The first one by direct line profile measurement yields v _ { r } = 300.3 \pm 5 \pm 6 km s ^ { -1 } for NGC 2006 and v _ { r } = 310.2 \pm 4 \pm 6 km s ^ { -1 } for SL 538 .
The second one is derived by comparing observed spectra with synthetic bootstrapped spectra yielding v _ { r } = 311.0 \pm 0.6 km s ^ { -1 } for NGC 2006 and v _ { r } = 309.4 \pm 0.5 km s ^ { -1 } for SL 538 .
Finally when spectra are directly compared , we find a \Delta v = 1.08 \pm 0.47 km s ^ { -1 } .
Full-spectrum SED fits reveal that the stellar population ages of both clusters lie in the range 13 - 21 Myr with a metallicity of Z = 0.008 .
We find indications for differences in the chemical abundance patterns as revealed by the helium absorption lines between the two clusters .
The dynamical analysis of the system shows that the two clusters are likely to merge within the next \sim 150 Myr to form a star cluster with a stellar mass of \sim 10 ^ { 4 } M _ { \odot }

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 \lesssim 20 km/s , 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 their formation may have taken place in a loosely bound star-formation complex which saw initial fragmentation but then had its clusters become a gravitationally bound pair by tidal capture .