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We provide a liquidity-based theory for the dominant use of the US dollar as the unit of denomination in global debt contracts. Firms need to trade their revenue streams for the assets required to extinguish their debt obligations. When asset markets are illiquid, as modeled via endogenous search frictions, firms optimally choose to denominate their debt in the unit of the asset that is easiest to obtain. This gives central importance to the denomination of government-backed assets with the largest safe, liquid, short-term float and to financial market institutions that facilitate safe asset creation. Equilibria with a single dominant currency emerge from a positive feedback cycle whereby issuing in the more liquid denomination endogenously raises its liquidity, incentivizing more issuance. We rationalize features of the current dollar-dominant international financial architecture and relate our theory to historical experiences, such as the prominence of the Dutch florin and pound sterling, the transition to the dollar, and the ongoing debate about the potential rise of the Chinese renminbi.