  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}. For a
direct comparison with chiral perturbation theory (ChPT), chiral symmetry is
exactly preserved by employing the overlap quark action. We utilize the
all-to-all quark propagator in order to calculate the scalar form factor
including the contributions of disconnected diagrams. A detailed comparison
with ChPT reveals that two-loop contributions are important to describe the
chiral behavior of the radii in our region of the pion mass M_\pi \gtrsim 290
MeV. From chiral extrapolation based on two-loop ChPT, we obtain <r^2>_V =
0.409(23)(37) fm^2 and <r^2>_S = 0.617(79)(66) fm^2, which are consistent with
phenomenological analyses.
