For a hierarchically constrained kinetic Ising chain it is shown that the p
rocess of spin-up propagation for small concentration c of facilitating up
spins occurs recursively near the bottom of the configuration space, which
has a self-similar structure. For chains with a finite number N of spins th
e spin autocorrelation Function is calculated analytically for N = 2 and 4
and numerically for N = 4 and 8. From the conjectured behaviour for arbitra
ry N it is concluded that the mean spin relaxation time tau(infinity) on th
e infinite chain for c --> 0 diverges more strongly than any positive power
of(1/c). (C) 1999 Published by Elsevier Science B.V. All rights reserved.