The reaction of (bipy)PdMe2 (1) (bipy = 2,2'-bipyridine) with molecular oxygen results in the formation of the palladium(II) methylperoxide complex (bipy)PdMe(OOMe) (2). The identity of the product 2 has been confirmed by independent synthesis. Results of kinetic studies of this unprecedented oxygen insertion reaction into a palladium alkyl bond support the involvement of a radical chain mechanism. Reproducible rates, attained in the presence of the radical initiator 2,2'-azobis(2-methylpropionitrile) (AIBN), reveal that the reaction is overall first-order (one-half-order in both [1] and [AIBN], and zero-order in [O-2]). The unusual rate law (half-order in [1]) implies that the reaction proceeds by a mechanism that differs significantly from those for organic autoxidations and for the recently reported examples of insertion of O-2 into Pd(II) hydride bonds. The mechanism for the autoxidation of 1 is more closely related to that found for the autoxidation of main group and early transition metal alkyl complexes. Notably, the chain propagation is proposed to proceed via a stepwise associative homolytic substitution at the Pd center of 1 with formation of a pentacoordinate Pd(III) intermediate.