A stochastic theory of muon spin relaxation in a model for muonium attached to trans-polyacetylene chains is given. The random walk of an unpaired electron provides a fluctuating hyperfine interaction with the muon. Since the correlation time of the stochastic process diverges, the standard NMR theory cannot be applied. The stochastic Liouville equation is solved, including spin flips of the electron. The resulting spin relaxation is nonexponential, and in reasonable agreement with the experimental data. The characteristic field dependence of one-dimensional diffusion is also contained in this theory.

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