  We investigate chiral properties of the overlap lattice fermion by using
solvable model in two dimensions, the gauged Gross-Neveu model. In this model,
the chiral symmetry is spontaneously broken in the presence of small but finite
fermion mass. We calculate the quasi-Nambu-Goldstone(NG) boson mass as a
function of the bare fermion mass and two parameters in the overlap formula. We
find that the quasi-NG boson mass has desired properties as a result of the
extended chiral symmetry found by L\"uscher. We also examine the PCAC relation
and find that it is satisfied in the continuum limit. Comparison between the
overlap and Wilson lattice fermions is made.
