We report the results of a mm-wave molecular line survey of the nearby (D ~ 70 pc), 12 Myr-old system V4046 Sgr -- a tight (9 R_sun separation), short-period (2.42 day) binary with nearly equal component masses of ~0.9 M_sun -- conducted with the 30 m telescope of the Institut de Radio Astronomie Millimetrique (IRAM). We detected rotational transitions of 12CO 13CO, 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 ~250 AU that is viewed at an inclination i = 35 degrees. We infer minimum disk gas and dust masses of ~13 and ~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 13CO is very optically thick. The overall similarity of the circumbinary disk of V4046 Sgr to the disk orbiting the single, ~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.
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