We have used a sample of high-resolution spectra obtained with the multi-fiber facility FLAMES at the Very Large Telescope of the European Southern Observatory , to derive the kinematical and chemical properties of the two young Large Magellanic Cloud globular clusters NGC 2136 and NGC 2137 . These two clusters represent a typical example of LMC cluster pair suspected to be bound in a binary system : indeed the cluster centers of gravity have an angular separation of less than 1.4 arcmin in the sky . The spectral analysis of seven giants in NGC 2136 and four in NGC 2137 reveals that the two clusters share very similar systemic radial velocities , namely V _ { r } = 271.5 \pm 0.4 km/s ( \sigma = 1.0 km/s ) and V _ { r } = 270.6 \pm 0.5 km/s ( \sigma = 0.9 km/s ) for NGC 2136 and NGC 2137 , respectively , and they have also indistinguishable abundance patterns . The iron content is [ Fe/H ] = -0.40 \pm 0.01 dex ( \sigma = 0.03 dex ) for NGC 2136 and -0.39 \pm 0.01 dex ( \sigma = 0.01 dex ) for NGC 2137 , while the [ \alpha /Fe ] ratios are roughly solar in both clusters . These findings suggest that the two clusters are gravitationally bound and that they formed from the fragmentation of the same molecular cloud that was chemically homogeneous . This is the first firm confirmation of the binary nature of a LMC cluster pair . The most likely fate of this system is to merge into a single structure in a time-scale comparable with its orbital period .