We report the results of a search for a point X-ray source (stellar remnant) in the southwest protrusion of the supernova remnant G315.4-2.30 (MSH 14-63, RCW 86) using the archival data of the Chandra X-ray Observatory. The search was motivated by a hypothesis that G315.4-2.30 is the result of an off-centered cavity supernova explosion of a moving massive star, which ended its evolution just near the edge of the main-sequence wind-driven bubble. This hypothesis implies that the southwest protrusion in G315.4-2.30 is the remainder of a pre-existing bow shock-like structure created by the interaction of the supernova progenitor's wind with the interstellar medium and that the actual location of the supernova blast center is near the center of this hemispherical structure. We have discovered two point X-ray sources in the ``proper" place. One of the sources has an optical counterpart with the photographic magnitude 13.38±0.40, while the spectrum of the source can be fitted with an optically thin plasma model. We interpret this source as a foreground active star of late spectral type. The second source has no optical counterpart to a limiting magnitude ∼21. The spectrum of this source can be fitted almost equally well with several simple models (power law: photon index =1.87; two-temperature blackbody: kT1=0.11keV, R1=2.34km and kT2=0.71keV, R2=0.06km; blackbody plus power law: kT=0.07keV, photon index =2.3). We interpret this source as a candidate stellar remnant (neutron star), while the photon index and non-thermal luminosity of the source (almost the same as those of the Vela pulsar and the recently discovered pulsar PSR J0205+6449 in the supernova remnant 3C 58) suggest that it can be a young ``ordinary" pulsar.