This paper explores various ways by which pixel disparities along epipolar rows of a stereo image pair could be obtained using Chebyshev moments of the corresponding 1D images. Chebyshev moments allow us to represent the image features based on orthogonal basis functions, and hence to reconstruct the intensity distribution from a set of moments fairly accurately. Disparity estimates can be obtained either analytically from the inverse moment transform, or by comparing the reconstructed intensity values. The paper also presents some preliminary results obtained using both synthetic and real images.