We present results of our Chandra observation with ACIS-I centered on the position of Sagittarius A ^ { * } ( Sgr A ^ { * } ) , the compact nonthermal radio source associated with the massive black hole ( MBH ) at the dynamical center of the Milky Way Galaxy . We have obtained the first high spatial resolution ( \approx 1 \arcsec ) , hard X-ray ( 0.5–7 keV ) image of the central 40 pc ( 17′ ) of the Galaxy . We have discovered an X-ray source , ( catalog CXOGC J174540.0 $ - $ 290027 ) , coincident with the radio position of Sgr A ^ { * } to within 0 \farcs 35 , corresponding to a maximum projected distance of 16 light-days for an assumed distance to the center of the Galaxy of 8.0 kpc . We received 222 \pm 17 ( 1 \sigma ) net counts from the source in 40.3 ks . The source is detected with high significance , S / N \simeq 37 \sigma , despite the highly elevated diffuse X-ray background in the central parsec of the Galaxy . Due to the low number of counts , the spectrum is well fit either by an absorbed power-law model with photon index \Gamma = 2.7 ^ { +1.3 } _ { -0.9 } ( N ( E ) \propto E ^ { - \Gamma } photons cm ^ { -2 } s ^ { -1 } keV ^ { -1 } ) and column density N _ { H } = ( 9.8 ^ { +4.4 } _ { -3.0 } ) \times 10 ^ { 22 } cm ^ { -2 } ( 90 % confidence interval ) or by an absorbed optically thin thermal plasma model with kT = 1.9 ^ { +0.9 } _ { -0.5 } keV and N _ { H } = ( 11.5 ^ { +4.4 } _ { -3.1 } ) \times 10 ^ { 22 } cm ^ { -2 } . Using the power-law model , the measured ( absorbed ) flux in the 2–10 keV band is ( 1.3 ^ { +0.4 } _ { -0.2 } ) \times 10 ^ { -13 } ergs cm ^ { -2 } s ^ { -1 } , and the absorption-corrected luminosity is ( 2.4 ^ { +3.0 } _ { -0.6 } ) \times 10 ^ { 33 } ergs s ^ { -1 } . The X-ray source coincident with Sgr A ^ { * } is resolved , with an apparent diameter of \approx 1 \arcsec . We report the possible detection , at the 2.7 \sigma significance level , of rapid continuum variability on a timescale of several hours . We also report the possible detection of an Fe K \alpha line at the \simeq 2 \sigma level . The long-term variability of Sgr A ^ { * } is constrained via comparison with the ROSAT /PSPC observation in 1992 . The origin of the X-ray emission ( MBH vs. stellar ) and the implications of our observation for the various proposed MBH emission mechanisms are discussed . The current observations , while of limited signal-to-noise , are consistent with the presence of both thermal and nonthermal emission components in the Sgr A ^ { * } spectrum . We also briefly discuss the complex structure of the X-ray emission from the Sgr A radio complex and along the Galactic plane and present morphological evidence that Sgr A ^ { * } and Sgr A West lie within the hot plasma in the central cavity of Sgr A East . Over 150 point sources are detected in the 17 \arcmin \times 17 \arcmin field of view . Our survey of X-ray sources is complete down to a limiting 2–10 keV absorbed flux of F _ { X } \approx 1.7 \times 10 ^ { -14 } ergs cm ^ { -2 } s ^ { -1 } . For sources at the distance of the Galactic Center , the corresponding absorption-corrected luminosity is L _ { X } \approx 2.5 \times 10 ^ { 32 } ergs s ^ { -1 } . The complete flux-limited sample contains 85 sources . Finally , we present an analysis of the integrated emission from the detected point sources and the diffuse emission within the central 0.4 pc ( 10″ ) of the Galaxy .