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(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 CosmologyTelescope collaboration as the strongest SZ decrement in its ~1000 sq. degsurvey. Our weak-lensing analysis confirms that ACT-CL J0102-4915 is indeed anextreme system consisting of two massive (~10^15 Msun each) subclusters with aprojected separation of ~0.7 Mpc. This binary mass structure revealed by ourlensing study is consistent with the cluster galaxy distribution and thedynamical study carried out with 89 spectroscopic members. We estimate the massof ACT-CL J0102-4915 by simultaneously fitting two axisymmetric NFW profilesallowing their centers to vary. Our MCMC analysis shows that the masses of thenorthwestern (NW) and the southeastern (SE) components are M200c=(1.38+-0.22) x10^15 Msun and (0.78+-0.20) x 10^15 Msun, respectively. The lensing-basedvelocity dispersions are consistent with their spectroscopic measurements. Thecentroids of both components are tightly constrained (~4") and close to theoptical luminosity centers. The X-ray and mass peaks are spatially offset by~8" (~62 kpc), which is significant at the ~2 sigma confidence level andconfirms that the baryonic and dark matter in this cluster are disassociated.The dark matter peak, however, does not lead the gas peak in the directionexpected if we are viewing the cluster soon after first core passage during ahigh speed merger. Under the assumption that the merger is happening in theplane of the sky, extrapolation of the two NFW halos to a radius r200a=2.4 Mpcyields a combined mass of M200a=(3.13+-0.56) x 10^15 Msun. This extrapolatedtotal mass is consistent with our two-component-based dynamical analysis andprevious X-ray measurements, projecting ACT-CL J0102-4915 to be the mostmassive cluster at z>0.6 known to date.

Weighing "El Gordo" with a Precision Scale: Hubble Space Telescope Weak-lensing Analysis of the Merging Galaxy Cluster ACT-CL J0102-4915 at z=0.87