We have used an automated Millikan oil drop method to search for free fractional-charge particles in a sample containing in total 3.9 mg of pulverized Allende meteorite suspended in 259 mg of mineral oil. The average diameter of the drops was 26.5 microm with the charge on about 42 500 000 drops being measured. This search was motivated by the speculation that isolatable, fractional-charge particles produced in the early Universe and present in our Solar System are more likely to be accumulated in asteroids than on Earth's surface. No evidence for fractional-charge particles was found. With 95% confidence, the concentration of particles with fractional-charge more than 0.25 e (e being the magnitude of the electron charge) from the nearest integer charge is less than 1.3 x 10(-21) particles per nucleon in the meteoritic material and less than 1.9 x 10(-23) particles per nucleon in the mineral oil.