Quasi-one-dimensional antiferromagnetic ͑AF͒ quantum spin systems show a wide range of interesting phenomena such as the spin-Peierls transition and disorder driven long-range ordering. While there is no magnetic long-range order in strictly one-dimensional systems, in real systems some amount of interchain coupling is always present and AF long-range order may appear below a Néel ordering temperature T N . We study the effect of bond randomness on Néel ordering in weakly coupled random AF Sϭ1/2 chains, both with and without dimerization ͑or spin-Peierls order͒. We use the real space renormalization group method to tackle the intrachain couplings, and a mean-field approximation to treat the interchain coupling. We show that in the nondimerized chain, disorder ͑represented by bond randomness͒ enhances the Néel order parameter; in the dimerized chain which shows no magnetic ordering in the weak interchain coupling limit without randomness, disorder can actually lead to long range order. Thus disorder is shown to lead to, or enhance the tendency toward long range order, providing another example of the order-by-disorder phenomenon. We make a qualitative comparison of our results with the observed phenomenon of doping induced long-range ordering in quasi-one-dimensional spin systems such as CuGeO 3 . Quasi-one-dimensional quantum spin systems have been under intense theoretical and experimental investigation over the past few decades.1 These systems show a wide range of interesting and unexpected phenomenon such as the spinPeierls transition and disorder driven long-range ordering.2-11 In strictly one-dimensional systems, there is no long-range magnetic order due to strong quantum and thermal fluctuations. However in real systems, such as CuGeO 3 , KCuF 3 , or Sr 2 CuO 3 some amount of interchain coupling is always present. 3,12,13 In these cases magnetic long range order may appear below a Néel ordering temperature T N . In this work we study the effect of disorder on long range ordering in weakly coupled spin chains. We show that disorder leads to, or enhances the tendency toward long-range order, providing another example of the order-by-disorder phenomenon that has received considerable attention in recent years.14 The disorder driven long-range ordering seen here is purely quantum mechanical in origin, as opposed to being thermally driven.14 The specific example that we bear in mind in our study is the interesting phenomenon of doping driven long range ordering observed in the spin-Peierls material CuGeO 3 . In this system the Cu ions form an effective one-dimensional ͑1D͒ antiferromagnetic ͑AF͒ spin-1/2 chain with weak interchain coupling. This is the first inorganic system to show the spinPeierls transition.3 Surprisingly, while the pure system has no magnetic order in the ground state, doping the system with a very small amount of impurities, such as Si for Ge ͑Refs. 4 -10͒ or Zn, Ni, or Mg for Cu, 4,5,8,11 leads to the appearance of AF long range order ͑LRO͒ that may coexist with spinPeierls order ͑or dimer...