We report Chandra observations of a double X-ray source in the z = 0.1569 galaxy SDSS J171544.05+600835.7. The galaxy was initially identified as a dual active galactic nucleus (AGN) candidate based on the double-peaked [O III] lambda 5007 emission lines, with a line-of-sight velocity separation of 350 km s(-1), in its Sloan Digital Sky Survey spectrum. We used the Kast Spectrograph at Lick Observatory to obtain two long-slit spectra of the galaxy at two different position angles, which reveal that the two Type 2 AGN emission components have not only a velocity offset, but also a projected spatial offset of 1.9 h(70)(-1) kpc on the sky. Chandra/ACIS observations of two X-ray sources with the same spatial offset and orientation as the optical emission suggest that the galaxy most likely contains Compton-thick dual AGNs, although the observations could also be explained by AGN jets. Deeper X-ray observations that reveal Fe K lines, if present, would distinguish between the two scenarios. The observations of a double X-ray source in SDSS J171544.05+600835.7 are a proof of concept for a new, systematic detection method that selects promising dual AGN candidates from ground-based spectroscopy that exhibits both velocity and spatial offsets in the AGN emission features.W.J. McDonald Postdoctoral FellowshipCollege of Natural SciencesDepartment of Astronomy at the University of Texas at AustinMcDonald ObservatoryU.S. Department of Energy DE-AC02-76SF00515Astronom