  We present an analysis of the active galaxy SDSS J131642.90+175332.5, which
is remarkable because all of its narrow emission lines are double-peaked, and
because it additionally shows an extra broad component (FHWM ~ 1400 km/s) in
most of its forbidden lines, peaking in between the two narrow systems. The
peaks of the two narrow systems are separated by 400--500 km/s in velocity
space. The spectral characteristics of double-peaked [O III] emission have
previously been interpreted as a signature of dual or binary active galactic
nuclei (AGNs), among other models. In the context of the binary scenario, SDSS
J131642.90+175332.5 is a particularly good candidate because not just one line
but all of its emission lines are double-peaked. However, we also discuss a
number of other scenarios which can potentially account for double-peaked
narrow emission lines, including projection effects, a two-sided outflow,
jet-cloud interactions, special narrow-line region (NLR) geometries (disks,
bars, or inner spirals), and a galaxy merger with only one AGN illuminating two
NLRs. We argue that the similarity of the emission-line ratios in both systems,
and the presence of the very unusual broad component at intermediate velocity,
makes a close pair of unrelated AGNs unlikely, and rather argues for processes
in a single galaxy or merger. We describe future observations which can
distinguish between these remaining possibilities.
