Value chain data is crucial for navigating economic disruptions. Yet, despite its importance, we lack publicly available product-level value chain datasets, since resources such as the “World Input-Output Database”, “Inter-Country Input-Output Tables”, “EXIOBASE”, and “EORA”, lack information about products (e.g. Radio Receivers, Telephones, Electrical Capacitors, LCDs, etc.) and instead rely on aggregate industrial sectors (e.g. Electrical Equipment, Telecommunications). Here, we introduce a method that leverages ideas from machine learning and trade theory to infer product-level value chain relationships from fine-grained international trade data. We apply our method to data summarizing the exports and imports of 1200+ products and 250+ world regions (e.g. states in the U.S., prefectures in Japan, etc.) to infer value chain information implicit in their trade patterns. In short, we leverage the idea that due to global value chains, regions specialized in the export of a product will tend to specialize in the import of its inputs. We use this idea to develop a novel proportional allocation model to estimate product-level trade flows between regions and countries. This contributes a method to approximate value chain data at the product level that should be of interest to people working in logistics, trade, and sustainable development.