  The anisotropic resistivity of PrBa$_2$Cu$_4$O$_8$ has been measured as a
function of electron irradiation fluence. Localization effects are observed for
extremely small amounts of disorder corresponding to electron mean-free-paths
of order 100 unit cells. Estimates of the localization corrections suggest that
this anomalous localization threshold heralds a crossover to a ground state
with pronounced one-dimensional character in which conduction electrons become
confined to a small cluster of chains.
