A high-sensitivity experiment was carred out to detect free quarks produced in collisions of 14.5-GeV/nucleon oxygen nuclei with a heavy target at BNL. Secondaries from the collisions were stopped in liquid-argon tanks, and charged atoms were collected electrostatically on goldcoated electrodes. The gold coatings were dissolved in a small drop of mercury, which was then tested for quarks in the San Francisco State University automated Millikan apparatus. No evidence for free fractional charge was found. The resulting upper limit is less than 1.0\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}9}$ quarks produced per incident $^{16}\mathrm{O}$ ion at 90% C.L.