  The supernova remnant (SNR) 3C 397 is thought to originate from a Type Ia
supernova (SN Ia) explosion of a near-Chandrasekhar-mass ($M_{\rm Ch}$)
progenitor, based on the enhanced abundances of Mn and Ni revealed by previous
X-ray study with Suzaku. Here we report follow-up XMM-Newton observations of
this SNR, conducted with the aim of investigating the detailed spatial
distribution of the Fe-peak elements. We have discovered an ejecta clump with
extremely high abundances of Ti and Cr, in addition to Mn, Fe, and Ni, in the
southern part of the SNR. The Fe mass of this ejecta clump is estimated to be
$\sim$ 0.06 $M_{\odot}$, under the assumption of a typical Fe yield for SNe Ia
(i.e., $\sim$ 0.8 $M_{\odot}$). The observed mass ratios among the Fe-peak
elements and Ti require substantial neutronization that is achieved only in the
innermost regions of a near-$M_{\rm Ch}$ SN Ia with a central density of
$\rho_c \sim 5 \times 10^9$ g cm$^{-3}$, significantly higher than typically
assumed for standard near-$M_{\rm Ch}$ SNe Ia ($\rho_c \sim 2 \times 10^9$ g
cm$^{-3}$). The overproduction of the neutron-rich isotopes (e.g., $^{50}$Ti
and $^{54}$Cr) is significant in such high-$\rho_c$ SNe Ia, with respect to the
solar composition. Therefore, if 3C 397 is a typical high-$\rho_c$ near-$M_{\rm
Ch}$ SN Ia remnant, the solar abundances of these isotopes could be reproduced
by the mixture of the high- and low-$\rho_c$ near-$M_{\rm Ch}$ and sub-$M_{\rm
Ch}$ Type Ia events, with $\lesssim$ 20 % being high-$\rho_c$ near-$M_{\rm
Ch}$.
