We study the stimulated Raman emission of a high-Q polydimethylsiloxane (PDMS)-coated silica microsphere on a silicon chip. In this hybrid structure, as the thickness of the PDMS coating increases, the spatial distribution of the whispering gallery modes moves inside the PDMS layer, and the light emission switches from silica Raman lasing to PDMS Raman lasing. The Raman shift of the PDMS Raman laser is measured at 2900 cm(-1), corresponding to the strongest Raman fingerprint of bulk PDMS material. The threshold for this PDMS Raman lasing is demonstrated to be as low as 1.3 mW. This type of Raman emission from a surface-coated high-Q microcavity not only provides a route for extending lasing wavelengths, but also shows potential for detecting specific analytes.