  In this letter we study the conductance G through one-dimensional quantum
wires with disorder configurations characterized by long-tailed distributions
(Levy-type disorder). We calculate analytically the conductance distribution
which reveals a universal statistics: the distribution of conductances is fully
determined by the exponent \alpha of the power-law decay of the disorder
distribution and the average < ln G >, i.e., all other details of the disorder
configurations are irrelevant. For 0< \alpha < 1 we found that the fluctuations
of ln G are not self-averaging and < ln G > scales with the length of the
system as L^\alpha, in contrast to the predictions of the standard
scaling-theory of localization where ln G is a self-averaging quantity and < ln
G > scales linearly with L. Our theoretical results are verified by comparing
with numerical simulations of one-dimensional disordered wires.
