We consider a multi-channel wireless network with flow-aware CSMA, which consists in running one instance of the CSMA algorithm per active flow. Specifically, each such instance attempts to access a randomly chosen radio channel after some random time and transmits a packet of the corresponding flow if the channel is sensed idle. We prove that, unlike the standard CSMA algorithm, this simple distributed access scheme is optimal in the sense that the network is stable for all traffic intensities in the capacity region of the network.