(Abridged) We present a HST weak-lensing study of the merging galaxy cluster El Gordo (ACT-CL J0102-4915) at z=0.87 discovered by the Atacama Cosmology Telescope collaboration as the strongest SZ decrement in its ~1000 sq. deg survey. Our weak-lensing analysis confirms that ACT-CL J0102-4915 is indeed an extreme system consisting of two massive (~10^15 Msun each) subclusters with a projected separation of ~0.7 Mpc. This binary mass structure revealed by our lensing study is consistent with the cluster galaxy distribution and the dynamical study carried out with 89 spectroscopic members. We estimate the mass of ACT-CL J0102-4915 by simultaneously fitting two axisymmetric NFW profiles allowing their centers to vary. Our MCMC analysis shows that the masses of the northwestern (NW) and the southeastern (SE) components are M200c=(1.38+-0.22) x 10^15 Msun and (0.78+-0.20) x 10^15 Msun, respectively. The lensing-based velocity dispersions are consistent with their spectroscopic measurements. The centroids of both components are tightly constrained (~4) and close to the optical luminosity centers. The X-ray and mass peaks are spatially offset by ~8 (~62 kpc), which is significant at the ~2 sigma confidence level and confirms that the baryonic and dark matter in this cluster are disassociated. The dark matter peak, however, does not lead the gas peak in the direction expected if we are viewing the cluster soon after first core passage during a high speed merger. Under the assumption that the merger is happening in the plane of the sky, extrapolation of the two NFW halos to a radius r200a=2.4 Mpc yields a combined mass of M200a=(3.13+-0.56) x 10^15 Msun. This extrapolated total mass is consistent with our two-component-based dynamical analysis and previous X-ray measurements, projecting ACT-CL J0102-4915 to be the most massive cluster at z>0.6 known to date.
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