We show that the spin chain/ladder compound La_3Sr_3Ca_8Cu_24O_41 is an insulator with hopping transport along the chains. In the temperature range 35 - 280 K, DC conductivity sigma_{DC}(T) follows Motts law of variable-range hopping conduction; the frequency dependence has the form sigma( u, T) = sigma_{DC}(T) + A(T) u^{s}, where s approx 1. The conduction mechanism changes from variable-range hopping to nearest-neighbor hopping around T_{c} =300 K. The chain array thus behaves like a one-dimensional disordered system. Disorder is due to random structural distortions of chains induced by irregular coordination of the La/Sr/Ca ions.
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