An experiment has been run at the Tevatron to search for stable fractionally charged particles (i.e., quarks) produced by the 800 GeV/c proton beam. The experiment was performed in two phases. In the first run, 1.0 x 10/sup 15/ protons passed through a series of four mercury targets which were distributed among several lead degraders. The lead degraders were arranged so that fractionally charged particles over a wide range of production angles, masses, and energies would stop in the mercury targets. A small amount of this mercury has been analyzed for fractional charge in an automated Millikan apparatus. A second run, which had an integrated proton intensity of 4.1 x 10/sup 13/, used liquid nitrogen tanks to stop any fractionally charged particles produced when the proton beam interacted in an upstream lead target. In the four tanks, electrically charged gold-plated glass fibers attracted and then trapped any fractional charges which were stopped in the liquid nitrogen. After the exposure, the wires were moved through small beads of mercury in which the gold was dissolved. One of these small beads of mercury also has been analyzed in the same Millikan apparatus. The results from the first run show that the uppermore » limit for quark production is less than 1 x 10/sup -6/ quarks per proton interaction at 90% confidence limit, the results from the second run show that the upper limit is 9.3 x 10/sup -10/. The analysis of the mercury is continuing.« less