Context : Direct information concerning the physical conditions and chemistry within the Jovian planet-building zones of circumbinary disks surrounding pre-main sequence stars is essentially nonexistent , especially for the more evolved pre-MS systems in which planets may already be forming or may have formed . Aims : We searched for a gaseous component within the dusty circumbinary disk around the nearby ( D \sim 70 pc ) , 12 Myr-old system V4046 Sgr — a tight ( 9 R _ { \odot } separation ) , short-period ( P \sim 2.42 day ) binary with nearly equal component masses of \sim 0.9 M _ { \odot } — so as to assess the mass , chemistry , and kinematics of this gaseous disk . Methods : We conducted a mm-wave molecular line survey of V4046 Sgr with the 30 m telescope of the Institut de Radio Astronomie Millimetrique ( IRAM ) . We use these data to investigate the kinematics , gas mass , and chemical constituents of the V4046 Sgr disk . Results : We detected rotational transitions of ^ { 12 } CO ^ { 13 } CO , HCN , CN , and HCO ^ { + } . The double-peaked CO line profiles of V4046 Sgr are well fit by a model invoking a Keplerian disk with outer radius of \sim 250 AU that is viewed at an inclination i = 35 ^ { \circ } . We infer minimum disk gas and dust masses of \sim 13 and \sim 20 Earth masses from the V4046 Sgr CO line and submm continuum fluxes , respectively . The actual disk gas mass could be much larger if the gas-phase CO is highly depleted and/or ^ { 13 } CO is very optically thick . Conclusions : The overall similarity of the circumbinary disk of V4046 Sgr to the disk orbiting the single , \sim 8 Myr-old star TW Hya — a star/disk system often regarded as representative of the early solar nebula — indicates that gas giant planets are likely commonplace among close binary star systems . Given the relatively advanced age and proximity of V4046 Sgr , these results provide strong motivation for future high-resolution imaging designed to ascertain whether a planetary system now orbits its twin suns .