Using a dual expression for the cut-off rate we derive an upper bound on the cut-off rate of an average- power limited discrete-time memoryless Rayleigh fading channel, where neither the transmitter nor the receiver knows the realization of the fading. The bound agrees asymptotically (as the signal-to-noise ratio tends to infinity) with a lower bound that we derive using the primal expression. This establishes that in this regime the cut-off rate is approximately 0.26 nats-per-channel-use away from capacity.