We present polarization profiles observed with the High Altitude Observatory/National Solar Observatory (HAO/NSO) Advanced Stokes Polarimeter (ASP) that demonstrate, in a model-independent way, the presence of strong downflows close to the neutral line of a delta sunspot (a spot with both polarities contained within the same penumbra). The flows are as large as 14 km/s, a velocity that, at photospheric levels, strongly suggests the presence of supersonic compressive fluid flows in a region only 100-200 km above the visible surface. These velocities are probably the largest ever reported at photospheric levels. The region containing the downflows is large enough (about 2 sec on a side) to be resolved, although it is likely to contain fine structure at or below our spatial resolution. The origin of these flows is discussed in terms of the funneling of material through an isolated magnetic nozzle in an otherwise closed magnetic system which is rising through the surface.