We present Kepler satellite photometry of KIC 10661783, a short-period binary star system which shows total eclipses and multiperiodic δ Scuti pulsations. A frequency analysis of the eclipse-subtracted light curve reveals at least 68 frequencies, of which 55 or more can be attributed to pulsation modes. The main limitation on this analysis is the frequency resolution within the 27-d short-cadence light curve. Most of the variability signal lies in the frequency range 18–31 d−1, with amplitudes between 0.1 and 4 mmag. One harmonic term (2f) and a few combination frequencies (fi+fj) have been detected. From a plot of the residuals versus orbital phase, we assign the pulsations to the primary star in the system. The pulsations were removed from the short-cadence data and the light curve was modelled using the Wilson–Devinney code. We are unable to get a perfect fit due to the residual effects of pulsations and also to the treatment of reflection and reprocessing in the light-curve model. A model where the secondary star fills its Roche lobe is favoured, which means that KIC 10661783 can be classified as an oEA system. Further photometric and spectroscopic observations will allow the masses and radii of the two stars to be measured to high precision and hundreds of δ Scuti pulsation frequencies to be resolved. This could lead to unique constraints on theoretical models of δ Scuti stars, if the evolutionary history of KIC 10661783 can be accounted for.