We present the first X-ray study of NGC6791, one of the oldest open clusters known (8 Gyr). Our Chandra observation is aimed at uncovering the population of close interacting binaries down to Lx ~ 1e30 erg/s (0.3-7 keV). We detect 86 sources within 8 arcmin of the cluster center, including 59 inside the half-mass radius. We identify twenty sources with proper-motion cluster members, which are a mix of cataclysmic variables (CVs), active binaries (ABs), and binaries containing sub-subgiants. With follow-up optical spectroscopy we confirm the nature of one CV. We discover one new, X-ray variable candidate CV with Balmer and HeII emission lines in its optical spectrum; this is the first X-ray--selected CV confirmed in an open cluster. The number of CVs per unit mass is consistent with the field, suggesting that the 3-4 CVs observed in NGC6791 are primordial. We compare the X-ray properties of NGC6791 with those of a few old open (NGC6819, M67) and globular clusters (47Tuc, NGC6397). It is puzzling that the number of ABs brighter than 1e30 erg/s normalized by cluster mass is lower in NGC6791 than in M67 by a factor ~3 to 7. CVs, ABs, and sub-subgiants brighter than 1e30 erg/s are under-represented per unit mass in the globular clusters compared to the oldest open clusters, and this accounts for the lower total X-ray luminosity per unit mass of the former. This indicates that the net effect of dynamical encounters may be the destruction of even some of the hardest (i.e. X-ray--emitting) binaries.
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