Starting in 2012, we began an unprecedented observational program focused on the supermassive black hole in the center of our Galaxy, Sgr A*, utilizing the High Energy Transmission Grating Spectrometer (HETGS) instrument on the Chandra X-Ray Observatory. These observations will allow us to measure the quiescent X-ray spectra of Sgr A* for the first time at both high spatial and spectral resolution. The X-ray emission of Sgr A*, however, is known to flare roughly daily by factors of a few to ten times over quiescent emission levels, with rarer flares extending to factors of greater than 100 times quiescence. Here we report an observation performed on 2012 February 9 wherein we detected what are the highest peak flux and fluence flare ever observed from Sgr A*. The flare, which lasted for 5.6 ks and had a decidedly asymmetric profile with a faster decline than rise, achieved a mean absorbed 2-8 keV flux of (8.5 ± 0.9) × 10-12 erg cm-2 s-1. The peak flux was 2.5 times higher, and the total 2-10 keV emission of the event was approximately 1039 erg. Only one other flare of comparable magnitude, but shorter duration, has been observed in Sgr A* by XMM-Newton in 2002 October. We perform spectral fits of this Chandra-observed flare and compare our results to the two brightest flares ever observed with XMM-Newton. We find good agreement among the fitted spectral slopes (Γ ~ 2) and X-ray absorbing columns (N H ~ 15 × 1022 cm-2) for all three of these events, resolving prior differences (which are most likely due to the combined effects of pileup and spectral modeling) among Chandra and XMM-Newton observations of Sgr A* flares. We also discuss fits to the quiescent spectra of Sgr A*.