We combine near-infrared imaging in two bands from the Hubble Space Telescope with archival observations of molecular gas to study SDSS J160705.16+533558.6 (J1607), an extremely luminous broad-line quasar at z = 3.65 that is also bright in the submillimeter. Via subtraction of the quasar point-spread function, we show that its host galaxy is massive, with a stellar mass of (5.8 ± 3.0) × 1011 M⊙, making it comparable to giant early-type galaxies (ETGs) at z ∼ 0. If the supermassive black hole in the quasar is accreting at the Eddington limit, then its mass is 3.5 × 109 M⊙, which is also consistent with local massive ETGs. The host has an extremely high star formation rate of 4300 ± 500 M⊙ yr−1 and a molecular gas mass of (2.4 ± 0.9) × 1010 M⊙. The quasar has two companions: one at a projected separation of 11 kpc with a stellar mass of (7.9 ± 5.0) × 1010 M⊙ but no detected molecular gas and one 6 kpc further away in the same direction with a molecular gas mass of (2.6 ± 1.3) × 1010 M⊙ but no detected stellar emission. Since neither companion shows evidence for active galactic nucleus activity, this may represent merger-driven quenching, in which the dynamics of the merger strip molecular gas from infalling galaxies. Overall, irrespective of whether the host is merging with the companions, these properties mark J1607 as forming what will become an extremely massive (∼1012 M⊙) galaxy by z = 0.