The orbital evolution of asteroidal fragments with diameters ranging from 10 cm to 20 km, injected into the 3:1 Kirkwood gap at 2.50 A.U., has been investigated using Monte Carlo techniques. It is assumed that this material can become Earth‐crossing on a time scale of 106years, as a result of a chaotic zone discovered by Wisdom, associated with the 3:1 resonance. This phenomenon, as well as close encounter planetary perturbations, the v6secular resonance, and the ablative effects of the Earth's atmosphere are included in the determination of the orbital characteristics of meteorites impacting the Earth derived by fragmentation of this asteroidal material. It is found that the predicted meteorite orbits closely match those found for observed ordinary chondrites, and the total flux is in approximate agreement with the observed fall rate of ordinary chondrites. About 10% of the predicted impacting bodies are meteorite‐size bodies originating directly from the asteroid belt. The remainder are obtained by subsequent fragmentation of larger (∼1 m to 20 km diameter) Earth‐crossing asteroidal fragments. The largest of these fragments are observable as Apollo‐Amor objects. Thus the apparent paradox between the orbital characteristics of observed ordinary chondrites and those predicted from Apollo object sources is reconciled. Both appear to be complementary aspects of the same phenomena. No other asteroidal resonance is found to be satisfactory as a source of ordinary chondrites. These meteorites are therefore most likely to be derived from S asteroids in this limited region of the asteroidal belt, the largest of which are 11 Parthenope, 17 Thetis, and 29 A