A theory is presented for forward- and backward-stimulated Raman scattering of colored chaotic light in dispersive media. Both amplification of a coherent Stokes seed and spontaneous generation are treated. It is shown that group-velocity dispersion reduces the gain for the average Stokes intensity, while the intensity fluctuations in the pump enhance it. For a given bandwidth, chaotic light is scattered more efficiently than coherent light when its average intensity exceeds the critical intensity for overcoming the decorrelating effects of group-velocity dispersion on the pump and Stokes waves. The figures presented demonstrate the asymmetry in the intensity of forward and backward Raman scattering of nonmonochromatic light.