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We have carried out a systematic search for recoiling supermassive black holes (rSMBH) using the Chandra Source and SDSS Cross-Match Catalog. From the survey, we have detected a potential rSMBH, CXO J101527.2 +625911, at z = 0.3504. The source CXO J101527.2+625911 has a spatially offset (1.26 +/- 0.05 kpc) active SMBH and kinematically offset broad emission lines (175 +/- 25 km s(-1) relative to the systemic velocity). The observed spatial and velocity offsets suggest that this galaxy could be an rSMBH, but we have also considered the possibility of a dual SMBH scenario. The column density toward the galaxy center was found to be Compton thin, but no X-ray source was detected. The non-detection of the X-ray source in the nucleus suggests that either there is no obscured actively accreting SMBH or that there exists an SMBH, but it has a low accretion rate (i.e., a low luminosity AGN (LLAGN)). The possibility of the LLAGN was investigated and found to be unlikely based on the Ha luminosity, radio power, and kinematic arguments. This, along with the null detection of an X-ray source in the nucleus, supports our hypothesis that CXO J101527.2+625911 is an rSMBH. Our GALFIT analysis shows the host galaxy to be a bulge-dominated elliptical. The weak morphological disturbance and small spatial and velocity offsets suggest that CXO J101527.2+625911 could be in the final stage of a merging process and about to turn into a normal elliptical galaxy.