  Renormalizability of a lattice chiral fermion is studied at one loop level in
the overlap formulation in four dimensions. The fermion chirality is examined
including the self-energy corrections due to gauge interactions. Divergent
terms breaking the chiral symmetry do not appear and the chiral fermion is
renormalized, preserving the correct chiral properties without adding new
counter-terms or tuning the parameters involved. The divergent part of the wave
function renormalization factor agrees with that of the continuum theory. The
overlap formulation of a lattice chiral fermion has passed the important test,
the renormalizability, at one loop level.
