In this paper we determine bounds of the capacity region of a two-user multiple-access channel with Rayleigh fading when neither the transmitters nor the receiver has channel state information (CSI). We assume that the fading coefficients as well as the additive noise are zero-mean complex Gaussian and there is an average power constraint at the channel input for both senders. Results that we get show that the lower (inner) and the upper (outer) bound of the capacity region are quite close for low and high signal-to-noise ratio (SNR). Surprisingly, the boundary of the capacity region is achieved by time sharing among users, which is not the case for fading channels with perfect CSI at the receiver. As an additional result we derive a closed form expression for the mutual information if the input is on-off binary. Index Terms− Multiple-access channel, capacity region, Rayleigh fading, channel state information, volume of the capacity region.