  The nucleon's axial vector charge, g_A, becomes delocalized in the chiral
limit. When m_\pi = 0, and SU(2)_L x SU(2)_R is exact, 1/3 of the nucleon's
axial charge is to be found at infinite distance from the nucleon. For finite
m_\pi this result is approached smoothly as m_\pi -> 0. We illustrate this
effect by considering the lepton-proton spin-spin interaction arising from Z^0
exchange as a function of m_\pi. Delocalization may have implications for
lattice calculations of g_A and in nuclei.
