Following the newly proposed idea of Currie et al., we have developed stochastic dynamics of a nonreflectionless soliton in a gas of phonons. The phase-shift interactions of the excitons and the solitary wave have been used for developing the mechanism of the Brownian motion of the soliton. The idea is to represent the soliton motion as a series of random collisions with the phonons. We have evaluated the random component of the velocity and the diffusion constant associated with the process.