From specific heat measurements in high quality H2@C60 samples performed over a broad temperature range, we obtain the smallest yet observed splitting of rotational energy sublevels of encapsulated single H2 molecules, 0.1-0.2 meV, in the nearly spherical potential well provided by highly isotropic C60 cages. Additionally, we find evidence of the quantized oscillation state of isolated H2 in the C60 cage. The minuscule splitting indicates that H2@C60 provides unprecedented opportunities to study free-molecule quantum dynamic properties.