Rollup protocols have recently received significant attention as a promising class of Layer 2 (L2) scalability solutions. By utilizing the Layer 1 (L1) blockchain solely as a bulletin board for a summary of the executed transactions and state changes, rollups enable secure off-chain execution while avoiding the complexity of other L2 mechanisms. However, to ensure data availability, current rollup protocols require the plaintext of executed transactions to be published on-chain, resulting in inherent privacy limitations. In this paper, we address this problem by introducing Calyx, the first privacy-preserving multi-token optimistic-Rollup protocol. Calyx guarantees full payment privacy for all L2 transactions, revealing no information about the sender, recipient, transferred amount, or token type. The protocol further supports atomic execution of multiple multi-token transactions and introduces a transaction fee scheme to enable broader application scenarios while ensuring the sustainable operation of the protocol. To enforce correctness, Calyx adopts an efficient one-step fraud-proof mechanism. We analyze the security and privacy guarantees of the protocol and provide an implementation and evaluation. Our results show that executing a single transaction costs approximately $0.06 (0.00002 ETH) and incurs only constant-size on-chain cost in asymptotic terms.