  We present a lattice calculation of $L_{10}$, one of the low energy constants
in Chiral Perturbation Theory, and the charged-neutral pion squared mass
splitting, using dynamical overlap fermion. Exact chiral symmetry of the
overlap fermion allows us to reliably extract these quantities from the
difference of the vacuum polarization functions for vector and axial-vector
currents. In the context of the technicolor models, these two quantities are
read as the $S$-parameter and the pseudo-Nambu-Goldstone boson mass
respectively, and play an important role in discriminating the models from
others. This calculation can serve as a feasibility study of the lattice
techniques for more general technicolor gauge theories.
