Standard state-machine replication involves consensus on a sequence of totally ordered requests through, for example, the Paxos protocol. Serialized request processing seriously limits our ability to leverage prevalent multi-core servers. This tension between concurrency and consistency is not inherent because the total-ordering of requests is merely a simplifying convenience that is unnecessary for consistency. Replicated state machines can be made parallel by consensus on partial-order traces, rather than on totally ordered requests, that capture causal orders in one replica execution and to be replayed in an order-preserving manner on others. The result is a new multi-core friendly replicated state-machine framework that achieves strong consistency while preserving parallelism in multi-threaded applications. On 12-core machines with hyper-threading, evaluations on typical applications show that we can scale with the number of cores, achieving up to a 16 times throughput increase over standard replicated state machines.