Recently, it has been shown that a simple, distributed CSMA algorithm can achieve throughput-optimality. However, the optimality is established under the ideal carrier sensing assumption, i.e., each link can precisely sense the presence of other active links in its neighborhood. This paper, in contrast, investigates the achievable throughput of the CSMA algorithm under imperfect carrier sensing. The main result is that CSMA can achieve an arbitrary fraction of the capacity region if certain access probabilities are set appropriately. To establish this result, we use the perturbation theory of Markov chains.