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We consider a disordered chain hosting quantum particles which form bipolarons due to coupling to magnetic excitations and study how the binding energy depends on the strength of disorder. We demonstrate that disorder may increase or decrease the binding energy, depending on the kinetic energy of particles as well as on the density of bipolarons and the range of pairing interaction. We show numerical results obtained for the t-J chains and for particles coupled to hard-core bosons and discuss simplified models which explain the essential physical mechanisms. We derive a formula for the dependence of the binding energy on disorder in the static limit.