State machine replication is a form of active replication commonly used to create fault-tolerant distributed services. In a nutshell, the approach consists in ensuring that a set of replicas receive and execute the same sequence of deterministic requests, returning the same results. This approach handles all requests evenly, but for some services it is important to consider that some requests have priority over others, i.e., that whenever two or more requests are ready to be executed, the one with higher priority is executed first. Paxos is perhaps the best known protocol to order requests in asynchronous environments, but Paxos has no notion of priority. In this paper we introduce the notion of priority-based state machine replication and modify Paxos to take request priorities into account. The proposed algorithm, PRaxos, works in three steps and satisfies Paxos' safety properties in asynchronous systems, while enforcing priorities when the system behaves synchronously.