Using Chandra, we have obtained imaging X-ray spectroscopy of the 10-16 Myr old F-star binary HD 113766. We individually resolve the 1 4 separation binary components for the first time in the X-ray and find a total 0.3-2.0 keV luminosity of 2.2×10 29 erg s −1 , consistent with previous RASS estimates. We find emission from the easternmost, infrared-bright, dusty member HD 113766A to be only ∼10% that of the western, infrared-faint member HD 113766B. There is no evidence for a 3rd late-type stellar or substellar member of HD 113766 with L x >6×10 25 erg s −1 within 2′ of the binary pair. The ratio of the two stars' X-ray luminosity is consistent with their assignments as F2V and F6V by Pecaut et al. The emission is soft for both stars, kT Apec =0.30-0.50 keV, suggesting X-rays produced by stellar rotation and/or convection in young dynamos, but not accretion or outflow shocks, which we rule out. A possible 2.8±0.15 (2σ) hr modulation in the HD 113766B X-ray emission is seen, but at very low confidence and of unknown provenance. Stellar wind drag models corresponding to L x ∼2×10 29 erg s −1 argue for a 1 mm dust particle lifetime around HD 113766B of only ∼90,0000 years, suggesting that dust around HD 113766B is quickly removed, whereas 1 mm sized dust around HD 113766A can survive for >1.5×10 6 years. At 10 28 -10 29 erg s −1 X-ray luminosity, astrobiologically important effects, like dust warming and X-ray photolytic organic synthesis, are likely for any circumstellar material in the HD 113766 systems.