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Field star BD+20 307 is the dustiest known main-sequence star, based on the fraction of its bolometric luminosity, ~4%, that is emitted at infrared wavelengths. The particles that carry this large infrared luminosity are unusually warm, comparable to the temperature of the zodiacal dust in the solar system, and their existence is likely to be a consequence of a fairly recent collision of large objects such as planets or planetary embryos. Thus, the age of BD+20 307 is potentially of interest in constraining the era of terrestrial planet formation. The present project was initiated with an attempt to derive this age using the Chandra X-Ray Observatory to measure the X-ray flux of BD+20 307 in conjunction with extensive photometric and spectroscopic monitoring observations from Fairborn Observatory. However, the recent realization that BD+20 307 is a short-period, double-line, spectroscopic binary whose components have very different lithium abundances vitiates standard methods of age determination. We find the system to be metal-poor; this, combined with its measured lithium abundances, indicates that BD+20 307 may be several to many Gyr old. BD+20 307 affords astronomy a rare peek into a mature planetary system in orbit around a close binary star (because such systems are not amenable to study by the precision radial velocity technique).