We present lens models for J1721+8842, the first-ever discovered galaxy-scale strong lens in an Einstein zigzag configuration. The model consists of four separate lensed galaxies, with the primary source hosting a quasar, lensed into six images by two deflectors at redshifts z1 = 0:184 and z2 = 1:885. The configuration of three lensed sources and the lensed light of the deflector at redshift z2 = 1:885 tightly constrain the mass profile of the primary lensing galaxy. Using two standard descriptions for the main perturbers mass distribution - a total power-law profile and a composite dark and stellar mass - the inferred convergence around the location of the lensed images is in excellent agreement. While the strong lensing data alone does not significantly favor either of our profile assumptions for the main deflectors mass distribution, we show that a central stellar velocity dispersion measurement can distinguish or validate them. Using a standard ΛCDM cosmology with H0 = 70 km s-1 Mpc-1, we present time-delay predictions between the lensed quasar images for both models at the percent level modulo a multiplane mass sheet transform. Our models are the first step toward constraining the time-delay distance ratios for J1721+8842, and thus also H0, independent of other methods. In order to achieve an H0 measurement, our models need to be combined in a multiplane lensing analysis with the stellar velocity dispersion for the deflectors, the line-of-sight convergence, and the observed time delays. Owing to its extraordinary configuration, this is an extremely promising system for a high-precision determination of H0.