This paper examines the impact of thin capitalization rules that limit the tax deductibility of interest on the capital structure of the foreign affiliates of US multinationals. We construct a new data set on thin capitalization rules in 54 countries for the period 1982-2004. Using confidential data on the internal and total leverage of foreign affiliates of US multinationals, we find that thin capitalization rules affect multinational firm capital structure in a significant way. Specifically, restrictions on an affiliate's debt-to-assets ratio reduce this ratio on average by 1.9%, while restrictions on an affiliate's borrowing from the parent-to-equity ratio reduce this ratio by 6.3%. Also, restrictions on borrowing from the parent reduce the affiliate's debt to assets ratio by 0.8%, which shows that rules targeting internal leverage have an indirect effect on the overall indebtedness of affiliate firms. The impact of capitalization rules on affiliate leverage is higher if their application is automatic rather than discretionary. Furthermore, we show that thin capitalization regimes have aggregate firm effects: they reduce the firm's aggregate interest expense bill but lower firm valuation. Overall, our results show than thin capitalization rules, which thus far have been understudied, have a substantial effect on the capital structure within multinational firms, with implications for the firm's market valuation.