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We derive the outage capacity region of an M-user fading multiple-access channel (MAC) under the assumption that both the transmitters and the receiver have perfect channel side information (CSI). The outage capacity region is implicitly obtained by deriving the outage probability region for a given rate vector. Given a required rate and average power constraint for each user, we find a successive decoding strategy and a power allocation policy that achieves points on the boundary of the outage probability region. We discuss the scenario where an outage must be declared simultaneously for all users (common outage) and when outages can be declared individually (individual outage) for each user.