  We present the discovery by the SPitzer InfraRed Intensive Transients Survey
(SPIRITS) of a likely supernova (SN) in NGC 3556 at only 8.8 Mpc, which,
despite its proximity, was not detected by optical searches. A luminous
infrared (IR) transient at $M_{[4.5]} = -16.7$ mag (Vega), SPIRITS 16tn is
coincident with a dust lane in the inclined, star-forming disk of the host.
Using IR, optical, and radio observations, we attempt to determine the nature
of this event. We estimate $A_V \approx$ 8 - 9 mag of extinction, placing it
among the three most highly obscured IR-discovered SNe to date. The [4.5] light
curve declined at a rate of 0.013 mag day$^{-1}$, and the $[3.6] - [4.5]$ color
grew redder from 0.7 to $\gtrsim$ 1.0 mag by 184.7 days post discovery.
Optical/IR spectroscopy shows a red continuum, but no clearly discernible
features, preventing a definitive spectroscopic classification. Deep radio
observations constrain the radio luminosity of SPIRITS 16tn to $L_{\nu}
\lesssim 10^{24}$ erg s$^{-1}$ Hz$^{-1}$ between 3 - 15 GHz, excluding many
varieties of radio core-collapse SNe. A type Ia SN is ruled out by the observed
red IR color, and lack of features normally attributed to Fe-peak elements in
the optical and IR spectra. SPIRITS 16tn was fainter at [4.5] than typical
stripped-envelope SNe by $\approx$ 1 mag. Comparison of the spectral energy
distribution to SNe II suggests SPIRITS 16tn was both highly obscured, and
intrinsically dim, possibly akin to the low-luminosity SN 2005cs. We infer the
presence of an IR dust echo powered by a peak luminosity of the transient of $5
\times 10^{40}$ erg s$^{-1} < L_{\mathrm{peak}} < 4\times10^{43}$ erg s$^{-1}$,
consistent with the observed range for SNe II. This discovery illustrates the
power of IR surveys to overcome the compounding effects of visible extinction
and optically sub-luminous events in completing the inventory of nearby SNe.
