We have detected a bright X-ray flare from the nearby brown dwarf LP 944-20 with the Chandra/ACIS-S. This is an old (500 Myr), rapidly rotating, lithium-bearing M9 object, with a bolometric luminosity of 6e29 ergs cm-2 s-1. It was only detected by Chandra during an X-ray flare of duration 1-2 hours near the end of a 12.1 hour observation. The peak X-ray luminosity was 1.2(+0.5/-0.3)e26 ergs cm-2 s-1 in the brightest ~550 seconds, corresponding to Lx/Lbol ~ 2e-4. A total of 2e29 ergs was

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... during the 43,773 sec observation, giving a time-averaged Lx/Lbol ~ 7e-6. LP 944-20 was not detected before the flare, with a 3 sigma upper limit on the emission at Lx/Lbol < 2e-6 (Lx<1e24 ergs cm-2 s-1). This is faint for a rapidly rotating late-type star, and establishes a record lower limit to the quiescent flux about an order of magnitude below the flux limit (and a factor of 5 below the Lx/Lbol limit) placed on quiescent X-ray emission from the M8 dwarf VB 10. The inferred flaring duty cycle is comparable to that measured via variable H-alpha emission for other late M-type, fully convective stars.