Cryptocurrency exchange platforms such as Coinbase, Binance, enable users to purchase and sell cryptocurrencies conveniently just like trading stocks/commodities. However, because of the nature of blockchain, when a user withdraws coins (i.e., transfers coins to an external on-chain account), all future transactions can be learned by the platform. This is in sharp contrast to conventional stock exchange where all external activities of users are always hidden from the platform. Since the platform knows highly sensitive user private information such as passport number, bank information etc, linking all (on-chain) transactions raises a serious privacy concern about the potential disastrous data breach in those cryptocurrency exchange platforms. In this paper, we propose a cryptocurrency exchange that restores user anonymity for the first time. To our surprise, the seemingly well-studied privacy/anonymity problem has several new challenges in this setting. Since the public blockchain and internal transaction activities naturally provide many non-trivial leakages to the platform, internal privacy is not only useful in the usual sense but also becomes necessary for regaining the basic anonymity of user transactions. We also ensure that the user cannot double spend, and the user has to properly report accumulated profit for tax purposes, even in the private setting. We give a careful modeling and efficient construction of the system that achieves constant computation and communication overhead (with only simple cryptographic tools and rigorous security analysis); we also implement our system and evaluate its practical performance.