Direct oxygenation of nonactivated aliphatic C(sp3)-H groups with peroxycarboxylic acids in the presence of palladium tris(pyridylmethyl)amine complex (0.6 mol %) is reported, providing the corresponding hydroxylated derivatives in up to 94% yields. The oxidation of 3° C-H groups occurs stereospecifically, with the catalyst system demonstrating extremely high sensitivity to electronic effects (adamantane oxidation: 3°:2° up to >300). This suggests potential applications for the 3°-regioselective oxidative functionalization of complex molecules of natural origin.