We investigate the transport properties of a one-dimensional (1D) chain with randomly side-coupled impurities.By using the transfer matrix technique, we present numerical results of the transmission coefficient as a function of the electron energy. It is found that an extended state will be shown in such a random 1D system if the impurities are side-coupled to the chain with not only the nearest-neighbour bonds but also the next-nearest-neighbour bonds. We present an analytical expression for the energy of this extended state, which is determined by the strength of the nearest and next-nearest couplings between the impurities and the chain. The obtained results can be used to explain the transport properties of DNA chains and other quasi-lD organic structures.
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