  We consider transient nearest-neighbor random walks in random environment on
Z. For a set of environments whose probability is converging to 1 as time goes
to infinity, we describe the fluctuations of the hitting time of a level n,
around its mean, in terms of an explicit function of the environment. Moreover,
their limiting law is described using a Poisson point process whose intensity
is computed. This result can be considered as the quenched analog of the
classical result of Kesten, Kozlov and Spitzer [Compositio Math. 30 (1975)
145-168].
