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We model the mass distribution in the recently discovered Einstein ring LBG J213512.73−010143 (the ‘Cosmic Eye’) using archival  Hubble Space Telescope  imaging. We reconstruct the mass density profile of the  z = 0.73 lens and the surface brightness distribution of the  z = 3.07 source and find that the observed ring is best fitted with a dual‐component lens model consisting of a baryonic Sersic component nested within a dark matter halo. The dark matter halo has an inner slope of 1.42 +0.24  −0.22 , consistent with cold dark matter simulations after allowing for baryon contraction. The baryonic component has a mass‐to‐light ratio of  1.71 +0.28  −0.38  M ⊙ /L  B   ⊙   which when evolved to the present day is in agreement with local ellipticals. Within the Einstein radius of 0.77 arcsec (5.6 kpc), the baryons account for 46 ± 11 per cent of the projected lens mass. External shear from a nearby foreground cluster is accurately predicted by the model. The reconstructed surface brightness distribution in the source plane clearly shows two peaks. Through a generalization of our lens inversion method, we conclude that the redshifts of both peaks are consistent with each other, suggesting that we are seeing structure within a single galaxy.

Separation of the visible and dark matter in the Einstein ring LBG J213512.73−010143