  Quantum Heisenberg spin chains with random couplings and spin sizes are
studied using a real-space renormalization group technique. These systems
belong to a new universality class of disordered quantum spin systems realized
in {\it e.g.} ${\rm Sr}_3{\rm CuPt}_{1-x}{\rm Ir}_x {\rm O}_6$. The low-energy
fixed point is characterized by the formation of weakly coupled large effective
spins. At low temperature $T$ the entropy obeys a power law $T^\delta$
($\delta\approx0.44$), and the susceptibility follows a Curie-like behavior.
