The quasar SDSS J153636.22+044127.0, exhibiting peculiar broad emission- line profiles with multiple components, was proposed as a candidate sub-parsec binary supermassive black hole system. More recently, imaging revealed two spatially distinct sources, leading some to suggest that the system was a quasar pair separated by åisebox-0.5ex 5 kpc. We present Palomar and Keck optical spectra of this system from which we identify a third velocity component to the emission lines. We argue that the system is more likely an unusual member of the class of active galactic nuclei known as ``double-peaked emitters’’ than a sub-parsec black hole binary or quasar pair. We find no significant velocity evolution of the two main peaks over the course of 0.95 yr, with a 3σ upper limit on any secular change of 70 km s$^-1$ yr$^-1$. We also find that the three velocity components of the emission lines are spatially coincident to within 0farcs015 along the slit, apparently ruling out the double-quasar hypothesis.