We consider transient random walks in random environment on \z with zero
asymptotic speed. A classical result of Kesten, Kozlov and Spitzer says that
the hitting time of the level n converges in law, after a proper
normalization, towards a positive stable law, but they do not obtain a
description of its parameter. A different proof of this result is presented,
that leads to a complete characterization of this stable law. The case of
Dirichlet environment turns out to be remarkably explicit.Comment: 31 pages, accepted for publication in "Annales de l'Institut Fourier
