  We present a quenched lattice calculation of the nucleon isovector vector and
axial-vector charges gV and gA. The chiral symmetry of domain wall fermions
makes the calculation of the nucleon axial charge particularly easy since the
Ward-Takahashi identity requires the vector and axial-vector currents to have
the same renormalization, up to lattice spacing errors of order O(a^2). The
DBW2 gauge action provides enhancement of the good chiral symmetry properties
of domain wall fermions at larger lattice spacing than the conventional Wilson
gauge action. Taking advantage of these methods and performing a high
statistics simulation, we find a significant finite volume effect between the
nucleon axial charges calculated on lattices with (1.2 fm)^3 and (2.4 fm)^3
volumes (with lattice spacing, a, of about 0.15 fm). On the large volume we
find gA = 1.212 +/- 0.027(statistical error) +/- 0.024(normalization error).
The quoted systematic error is the dominant (known) one, corresponding to
current renormalization. We discuss other possible remaining sources of error.
This theoretical first principles calculation, which does not yet include
isospin breaking effects, yields a value of gA only a little bit below the
experimental one, 1.2670 +/- 0.0030.
