Bound orbits have traditionally been assigned to the Large and Small Magellanic Clouds (LMC and SMC, respectively) in order to provide a formation scenario for the Magellanic Stream (MS) and its Leading Arm (LA), two prominent neutral hydrogen (HI) features connected to the LMC and SMC. However, Hubble Space Telescope (HST) measurements of the proper motions of the LMC and SMC have challenged the plausibility of bound orbits, causing the origin of the MS to re-emerge as a contested issue. We present a new tidal model in which structures resembling the bifurcated MS and elongated LA are able to form in a bound orbit consistent with the HST proper motions. The LMC and SMC have remained bound to each other only recently in our model despite being separately bound to the Milky Way for more than 5 Gyr. We find that the MS and LA are able to form as a consequence of LMC-dominated tidal stripping during the recent dynamical coupling of the LMC and SMC. Our orbital model depends on our assumption that the Milky Way has a constant circular velocity of Vcir= 250 km s−1 up to 160 kpc, which implies a massive isothermal halo that is not completely rejected by observations.