We report on a new measurement of the decay K-L --> pi(0)gamma gamma by the
KTeV experiment at Fermilab. We determine the K-L --> pi(0)gamma gamma bra
nching ratio to be (1.68 +/- 0.07 +/- 0.08) x 10(-6). Our data show the fir
st evidence for a low-mass gamma gamma signal as predicted by recent O(p(6)
) chiral perturbation calculations which include vector meson exchange cont
ributions. From our data, we extract a value for the effective vector coupl
ing a(V) = -0.72 +/- 0.05 +/- 0.06.