We present the first Laser Guide Star Adaptive Optics ( LGS-AO ) observations of the Galactic center . LGS-AO has dramatically improved the quality and robustness with which high angular resolution infrared images of the Galactic center can be obtained with the W. M. Keck II 10-meter telescope . Specifically , Strehl ratios of 0.7 and 0.3 at L ’ [ 3.8 \mu m ] and K ’ [ 2.1 \mu m ] , respectively , are achieved in these LGS-AO images ; these are at least a factor of two higher and a factor of four to five more stable against atmospheric fluctuations than the Strehl ratios delivered thus far with the Keck Natural Guide Star AO system on the Galactic center . Furthermore , these observations are the first that cover a large area ( 76 \arcsec \times 76 \arcsec ) surrounding the central black hole at diffraction-limited resolution for an 8-10 meter class telescope . During our observations , the infrared counterpart to the central supermassive black hole , Sgr A*-IR , showed significant infrared intensity variations , with observed L ’ magnitudes ranging from 12.6 to 14.5 mag and a decrease in flux density of a factor of two over an 8 minute interval . The faintest end of our L ’ detections , 1.3 mJy ( dereddened ) , is the lowest level of emission yet observed for this source by a factor of 3 . No significant variation in the location of SgrA*-IR is detected as a function of either wavelength or intensity . Previous claims of such positional variations are easily attributable to a nearby ( 0 \farcs 09 or 720 AU , projected ) , extended , very red source , which we suggest arises from a locally heated dust feature . Near a peak in its intensity , we obtained the first measurement of SgrA*-IR ’ s K ’ -L ’ color ; its K ’ -L ’ of 3.0 \pm 0.2 mag ( observed ) or 1.4 \pm 0.2 ( dereddened ) corresponds to an intrinsic spectral index of \alpha -0.5 \pm 0.3 for F _ { \nu } \sim \nu ^ { \alpha } . This is significantly bluer than other recent infrared measurements from the literature , which suggest \alpha = -4 \pm 1 . Because our measurement was taken at a time when Sgr A* was \sim 6 times brighter in the infrared than the other measurements , we posit that the spectral index of the emission arising from the vicinity of our Galaxy ’ s central black hole may depend on the strength of the flare , with stronger flares giving rise to a higher fraction of high energy electrons in the emitting region .