We have surveyed for Kuiper Belt objects (KBOs) in six fields of the ecliptic (total sky area 1.5 deg2) to limiting magnitudes between R=24.9 and R=25.9. This is deep enough to detect KBOs of diameter >~160 km at a distance of 65 AU. We detected 24 objects. None of these objects, however, is beyond 53 AU. Our survey places a 95% CL upper limit of Σ<5 deg-2 on the surface density of KBOs larger than ~160 km beyond 55 AU. This can be compared to the surface density of ~6 deg -2 of >=160 km KBOs at distances 30-50 AU determined from this survey and previous shallower surveys. The mean volume density of D>160 km KBOs in the 55-65 AU region is, at greater than 95% confidence, less than the mean density in the 30-50 AU region, and at most two-thirds of the mean density from 40 to 50 AU. Thus, a substantial density increase beyond 50 AU is excluded in this model-independent estimate. A dense primordial disk could be present beyond 50 AU if it contains only smaller objects or is sufficiently thin and inclined to have escaped detection in our six survey fields.