The stability domain for satellite orbits around Pluto extends ≈100 times further than the radius of Charon's orbit. We report here the results of a deep CCD imaging search for faint, distant satellites of Pluto. Our search was made in the region extending from 6 arcsec from Pluto to beyond the edge of Pluto's stability domain, during oppositions in 1990 and 1991. No detections were made, and we conservatively set 90%-confidence upper limits on the absence of potential satellites brighter than 20.6 ± 0.5 m in the region 6 to 10 arcsec from Pluto and brighter than 22.6 ± 0.5 m in the region from 10 arcsec to the edge of Pluto's stability domain. At the 90% confidence level this allows us to rule out the presence of any object with Charon-like albedo ( A = 0.4) with a radius > 58 ± 19 km in the region 6-10 arcsec from Pluto. Objects more than 10 arcsec from Pluto with a radius > 23 ± 8 km and Charon- like albedo can also be virtually excluded. These results provide the strongest constraints yet on distant satellites of Pluto.