  Chiral perturbation theory supplemented by the Omnes function is employed to
study the strength of the isoscalar central nuclear interaction, G_S, in the
chiral limit vs the physical case. A very large modification is seen, i.e.
eta_s = G_S ~ chiral /G_S ~ physical = 1.37 +- 0.10 . This large effect is seen
to arise dominantly at low energy from the extra contributions made by massless
pions at energies near the physical threshold where the physical spectral
function must vanish kinematically. The slope away from the chiral limit, d_S,
is also calculated and is correspondingly large. I also explain why this large
variation is to be expected.
