We have identified counterparts to two submillimeter (submm) sources, SMM J09429+4659 and SMM J09431+4700, seen through the core of the z = 0.41 cluster A851. We employ deep 1.4 GHz observations and the far-infrared/radio correlation to refine the submm positions and then optical and near-infrared imaging to locate their counterparts. We identify an extremely red counterpart to SMM J09429+4659, while Gemini Multi-Object Spectrograph spectroscopy with Gemini North shows that the R = 23.8 radio source identified with SMM J09431+4700 is a hyperluminous infrared galaxy (LFIR ~ 1.5 × 1013 L☉) at z = 3.35, the highest spectroscopic redshift so far for a galaxy discovered in the submm. The emission-line properties of this galaxy are characteristic of a narrow-line Seyfert 1 galaxy, although the lack of detected X-ray emission in a deep XMM-Newton observation suggests that the bulk of the luminosity of this galaxy is derived from massive star formation. We suggest that active nuclei, and the outflows they engender, may be an important part of the evolution of the brightest submm galaxies at high redshifts.