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 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 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, and the color grew redder from 0.7 to 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 $L_{\nu} \lesssim 10^{24}^{-1}^{-1}$ 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 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 $5 \times 10^{40}^{-1} < L_{} < 4\times10^{43}^{-1}$, 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.

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