Highly precise and nearly uninterrupted optical photometry of the RR Lyrae star AQ Leo was obtained with the MOST (Microvariability and Oscillations of Stars) satellite over 34.4 d in 2005 February-March. AQ Leo was the first known double-mode RR Lyrae pulsator (RRd star). Three decades after its discovery, MOST observations have revealed that AQ Leo oscillates with at least 42 frequencies, of which 32 are linear combinations (up to the sixth order) of the radial fundamental mode and its first overtone. Evidence for period changes of these modes is found in the data. The other intrinsic frequencies may represent an additional non-radial pulsation mode and its harmonics (plus linear combinations) which warrant theoretical modelling. The unprecedented number of frequencies detected with amplitudes down to mmag precision also presents an opportunity to test non-linear theories of mode growth and saturation in RRd stars.