  We present a new perturbative real space renormalization group (RG) to study
random quantum spin chains and other one-dimensional disordered quantum
systems. The method overcomes problems of the original approach which fails for
quantum random chains with spins larger than S=1/2. Since it works even for
weak disorder we are able to obtain the zero temperature phase diagram of the
random antiferromagnetic Heisenberg spin-1 chain as a function of disorder. We
find a random singlet phase for strong disorder and as disorder decreases, the
system shows a crossover from a Griffiths to a disordered Haldane phase.
