Foreign direct investment (FDI) in developing countries is often associated with higher economic growth due to knowledge and technology spillovers to local firms. One way how FDI speeds up growth is that it facilitates the manufacturing of more sophisticated products by local firms. So far, firm-level evidence is missing on how the presence of multinational firms affects the product sophistication of firms in a developing country. This paper aims to fill this gap. We compile an extensive firm-product-level dataset of Indian manufacturing firms which we complement with information on product sophistication and spillovers from FDI. We then explore different channels through which spillovers from multinationals to local Indian firms foster the manufacturing of sophisticated products. We find evidence that spillovers through supplier linkages strongly increase the manufacturing of sophisticated products in India.