Conventional descriptions of polymers in random media often characterize the disorder by way of a spatially random potential. When averaged, the potential produces an effective attractive interaction between chain segments that can lead to chain collapse. As an alternative to this approach, we consider here a model in which the effects of disorder are manifested as a random alternation of the Kuhn length of the polymer between two average values. A path integral formulation of this model gene:rates an effective Hamiltonian whose interaction term (representing the disorder in the medium) is quadratic and nonlocal in the spatial coordinates of the monomers. The average end-to-end distance of the chain is computed exactly as a function of the ratio of the two Kuhn lengths for different values of the frequency of alternation. For certain parameter values, chain contraction is found to occur to a state that is chain length dependent. In both the expanded and compact configurations, the scaling exponent that characterizes this dependence is found to be the same.