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We empirically characterize how China is internationalizing the Renminbi by selectively opening up its domestic bond market to foreign investors and propose a dynamic reputation model to explain this internationalization strategy. The Chinese government deliberately controlled the entry of foreign investors into its market, first allowing in relatively stable long-term investors like central banks before allowing in flightier investors like mutual funds. Our framework explains these patterns as the result of a government strategy to build its reputation as an international currency issuer while attempting to reduce the cost of potential capital flight as it tries to gain credibility. The dynamics of reputation make Chinese debt a substitute for emerging market risky debt in the early stage of internationalization and more of a substitute for developed countries safe debt in the later stages. We extend our framework to explore how countries compete to become a reserve currency. Competition worsens the incentives to build up reputation by reducing the benefits of having a higher reputation. The framework is tractable and can make sense of both new entrants like China and established players like the United States.