Monero provides a high level of anonymity for both users and their transactions. However, many criminal activities might be committed with the protection of anonymity in cryptocurrency transactions. Thus, user accountability (or traceability) is also important in Monero transactions, which is unfortunately lacking in the current literature. In this paper, we fill this gap by introducing a new cryptocurrency named Traceable Monero to balance the user anonymity and accountability. Our framework relies on a tracing authority, but is optimistic, in that it is only involved when investigations in certain transactions are required. We formalize the system model and security model of Traceable Monero. We present a detailed construction of Traceable Monero by overlaying Monero with two types of tracing mechanisms, tracing the one-Time addresses with money flows and tracing the long-Term addresses. We prove the security of Traceable Monero and implement a prototype of the system, which demonstrates that Traceable Monero incurs merely a very small overhead in generating and verifying a transaction compared to Monero transactions.