The X-ray source CXOXBJ142607.6+353351 (CXOJ1426+35), which was identified in a 172 ks Chandra image in the Bootes field, shows double-peaked rest-frame optical/UV emission lines, separated by 0.69 (5.5 kpc) in the spatial dimension and by 690 km s^-1 in the velocity dimension. The high excitation lines and emission line ratios indicate both systems are ionized by an AGN continuum, and the double-peaked profile resembles that of candidate dual AGN. At a redshift of z=1.175, this source is the highest redshift candidate dual AGN yet identified. However, many sources have similar emission line profiles for which other interpretations are favored. We have analyzed the substantial archival data available in this field, as well as acquired near-infrared (NIR) adaptive optics (AO) imaging and NIR slit spectroscopy. The X-ray spectrum is hard, implying a column density of several 10^23 cm^-2. Though heavily obscured, the source is also one of the brightest in the field, with an absorption-corrected 2-10 keV luminosity of ~10^45 erg s^-1. Outflows driven by an accretion disk may produce the double-peaked lines if the central engine accretes near the Eddington limit. However, we may be seeing the narrow line regions of two AGN following a galactic merger. While the AO image reveals only a single source, a second AGN would easily be obscured by the significant extinction inferred from the X-ray data. Understanding the physical processes producing the complex emission line profiles seen in CXOJ1426+35 and related sources is important for interpreting the growing population of dual AGN candidates.