  We propose a new formulation of chiral fermions on a lattice, on the basis of
a lattice extension of the covariant regularization scheme in continuum field
theory. The species doublers do not emerge. The real part of the effective
action is just one half of that of Dirac-Wilson fermion and is always gauge
invariant even with a finite lattice spacing. The gauge invariance of the
imaginary part, on the other hand, sets a severe constraint which is a lattice
analogue of the gauge anomaly free condition. For real gauge representations,
the imaginary part identically vanishes and the gauge invariance becomes exact.
