We determine the bit-error-rate (BER) of multi-level quadrature amplitude modulation (M-QAM) in flat Rayleigh fading with imperfect channel estimates. Despite its high spectral efficiency, M-QAM is not commonly used over fading channels because of the channel amplitude and phase variation. Since the decision regions of the demodulator depend on the channel fading, estimation error of the channel variation can severely degrade the demodulator performance. Among the various fading estimation techniques, pilot symbol assisted modulation (PSAM) proves to be an effective choice. We first characterize the distribution of the amplitude and phase estimates using PSAM. We then use this distribution to obtain the BER of M-QAM as a function of the PSAM and channel parameters. By using a change of variables our exact BER expression has a particularly simple form that involves just a few finite range integrals. This approach can be used to compute BER for any value of M. We compute the BER for 16-QAM and 64-QAM numerically and verify our analytical results by computer simulation. We show that for these modulations, amplitude estimation error leads to a 1 dB degradation in Eb/No and combined amplitude-phase estimation error leads to 2.5 dB degradation for the parameters we consider.