We have imaged the disk surrounding the nearby ( D \sim 73 pc ) , \sim 12 Myr , classical T Tauri binary system V4046 Sgr with the Submillimeter Array ( SMA ) at an angular resolution of \sim 2″ . We detect a rotating disk in ^ { 12 } CO ( 2–1 ) and ^ { 13 } CO ( 2–1 ) emission , and resolve the continuum emission at 1.3 mm . We infer disk gas and dust masses of \sim 110 and \sim 40 Earth masses , respectively . Fits to a power-law disk model indicate that the molecular disk extends to \sim 370 AU and is viewed at an inclination of between \sim 33 ^ { \circ } and \sim 39 ^ { \circ } for dynamical stellar masses ranging from 1.8 M _ { \odot } down to 1.5 M _ { \odot } ( the range of total mass previously determined for the central , 2.4 day spectroscopic binary ) . This range of disk inclination is consistent with that assumed in deducing the central binary mass ( i.e. , 35 ^ { \circ } ) , suggesting that the V4046 Sgr binary system and its circumbinary , molecular disk are coplanar . In light of the system ’ s age and binarity , the presence of an extensive molecular disk orbiting V4046 Sgr provides constraints on the timescales of processes related to Jovian planet formation , and demonstrates that circumbinary Jovian planets potentially could form around close binary systems .