An ideal antiferromagnetic (AF) ordering of the spins of the CuO layer
s of an under-doped cuprate prevents the low energy tunneling of the c
harge carriers between the layers. In order to obtain a non-vanishing
c-axis conductivity (sigma(c)), we invoke ground state fluctuations of
the spin system. These provide a frequency-dependent,eating effect by
changing the direction of the AF order parameter within one layer rel
ative to that in a neighboring layer, thereby permitting some tunnelin
g. The calculated sigma(c) compares favorably with experimental data i
n a) being small and b) having a weak frequency dependence of distinct
ly non-Drude form.