The use of polynomial chaos for incorporating environmental variability into propagation models is investigated in the context of a simplified one-dimensional model, which is relevant for acoustic propagation when the random sound speed is independent of depth. Environmental variability is described by a spectral representation of a stochastic process and the chaotic representation of the wave field then consists of an expansion in terms of orthogonal random polynomials. Issues concerning implementation of the relevant equations, the accuracy of the approximation, uniformity of the expansion over the propagation range, and the computational burden necessary to evaluate different field statistics are addressed. When the correlation length of the environmental fluctuations is small, low-order expansions work well, while for large correlation lengths the convergence of the expansion is highly range dependent and requires high-order approximants. These conclusions also apply in higher-dimensional propagation problems.