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Recent observations have shown a remarkable diversity of observational behaviors and explosion mechanisms in thermonuclear supernovae (SNe). An emerging class of peculiar thermonuclear SNe, called Type Iax, show photometric and spectroscopic behaviors distinct from normal Type Ia. Their origin remains highly controversial, but pure turbulent deflagration of white dwarfs (WDs) has been regarded as the leading formation theory. The large population of Type Iax indicates the existence of unidentified Galactic Type Iax supernova remnants (SNRs). We report evidence that SNR Sgr A East in the Galactic center resulted from a pure turbulent deflagration of a Chandrasekhar-mass carbon-oxygen WD, an explosion mechanism used for Type Iax SNe. Our X-ray spectroscopic study of Sgr A East using 3 Ms of Chandra data shows a low ratio of intermediate-mass elements to Fe and large Mn/Fe and Ni/Fe ratios. This abundance pattern does not accord with the core-collapse or normal Type Ia models. Sgr A East is thus the first Galactic SNR for which a likely Type Iax origin has been proposed and the nearest target for studying this peculiar class. We compared Sgr A East with the Fe-rich SNRs 3C 397 and W49B, which also have high Mn and Cr abundances and were claimed to result from deflagration-to-detonation explosions of Chandrasekhar-mass WDs (although with disputes). Our study shows that they have distinct abundance patterns. The X-ray spectroscopic studies of thermonuclear SNRs provide observational evidence for the theories that there are diverse explosion channels and various metal outputs for Chandrasekhar-mass WDs.