Statistical mechanics (SM) of Yang-Mills classical mechanics is studied by using a toy model that resembles chaotic quartic oscillators. This nonlinear system attains the thermodynamic equilibrium not by collisions, which is generally assumed in SM, but by chaotic dynamics. This is a new mechanism of thermalization that may be relevent to the quark-gluon plasma (QGP) formation in relativistic heavy-ion collisions because the interactions governing QGP involve quantum chromodynamics (QCD), which is a Yang-Mills theory [SU(3)]. The thermalization time is estimated from the Lyapunov exponent. The Lyapunov exponent is evaluated using the recently developed monodromy matrix method. We also discuss the physical meaning of thermalization and SM in this system of few degrees in terms of chromo-electric and chromomagnetic fields. One of the consequence of thermalization, such as equipartition of energy and dynamical temperature, is also numerically verified.