  We study the reducibility of a Linear Schr\"odinger equation subject to a
small unbounded almost-periodic perturbation which is analytic in time and
space. Under appropriate assumptions on the smallness, analiticity and on the
frequency of the almost-periodic perturbation, we prove that such an equation
is reducible to constant coefficients via an analytic almost-periodic change of
variables. This implies control of both Sobolev and Analytic norms for the
solution of the corresponding Schr\"odinger equation for all times.
