  We calculate pion vector and scalar form factors in two-flavor lattice QCD
and study the chiral behavior of the vector and scalar radii <r^2>_{V,S}.
Numerical simulations are carried out on a 16^3 x 32 lattice at a lattice
spacing of 0.12 fm with quark masses down to \sim m_s/6, where m_s is the
physical strange quark mass. Chiral symmetry, which is essential for a direct
comparison with chiral perturbation theory (ChPT), is exactly preserved in our
calculation at finite lattice spacing by employing the overlap quark action. We
utilize the so-called all-to-all quark propagator in order to calculate the
scalar form factor including the contributions of disconnected diagrams and to
improve statistical accuracy of the form factors. A detailed comparison with
ChPT reveals that the next-to-next-to-leading-order contributions to the radii
are essential to describe their chiral behavior in the region of quark mass
from m_s/6 to m_s/2. Chiral extrapolation based on two-loop ChPT yields
<r^2>_V=0.409(23)(37)fm and <r^2>_S=0.617(79)(66)fm, which are consistent with
phenomenological analysis. We also present our estimates of relevant low-energy
constants.
