Despite their importance, a detailed understanding of Type Ia supernovae (SNe Ia) remains elusive. X-ray measurements of the element distributions in supernova remnants (SNRs) offer important clues for understanding the explosion and nucleosynthesis mechanisms for SNe Ia. However, it is challenging to observe the entire ejecta mass in X-rays for young SNRs, because the central ejecta may not have been heated by the reverse shock yet. Here we present over 200 kilosecond Chandra observations of the Type Ia SNR G344.7-0.1, whose age is old enough for the reverse shock to have reached the SNR center, providing an opportunity to investigate the distribution of the entire ejecta mass. We reveal a clear stratification of heavy elements with a centrally peaked distribution of the Fe ejecta surrounded by intermediate-mass elements (IMEs: Si, S, Ar Ca) with an arc-like structure. The centroid energy of the Fe K emission is marginally lower in the central Fe-rich region than in the outer IME-rich regions, suggesting that the Fe ejecta were shock-heated more recently. These results are consistent with the prediction for standard SN Ia models, where the heavier elements are synthesized in the interior of an exploding white dwarf. We find, however, that the peak location of the Fe K emission is slightly offset to the west with respect to the geometric center of the SNR. This apparent asymmetry is likely due to the inhomogeneous density distribution of the ambient medium, consistent with our radio observations of the ambient molecular and neutral gas.