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Traditional mutual exclusion locks are not resilient to failures: if there is a power outage, the memory is wiped out. Thus, when the system comes back on, the lock will have to be restored to the initial state, i.e., all processes are rolled back to the Remainder section and all variables are reset to their initial values. Recently, Golab and Ramaraju showed that we can improve this state of the art by exploiting the Non-Volatile RAM (NVRAM). They designed algorithms that, by maintaining shared variables in NVRAM, allow processes to recover from crashes on their own without a need for a global reset, even though a crash can wipe out the local memory of a process. We present a Recoverable Mutual Exclusion algorithm using the commonly supported CAS primitive. The main features of our algorithm are that it satisfies FCFS, it ensures that each process recovers in a wait-free manner, and in the absence of failures, it guarantees a worst-case Remote Memory Reference (RMR) complexity of O(lg n) on both Cache Coherent (CC) and Distributed Shared Memory (DSM) machines, where n is the number of processes for which the algorithm is designed. This bound matches the Omega(lg n) RMR lower bound by Attiya, Hendler, and Woelfel for Mutual Exclusion algorithms that use comparison primitives.