This work presents the results obtained on HD 50844, the only delta Sct star observed in the CoRoT Initial Run (57.6d). The aim of these CoRoT observations was to investigate and characterize for the first time the pulsational behaviour of a delta Sct star, when observed at a level of precision and with a much better duty cycle than from the ground. The 140016 datapoints were analysed using independent approaches (SigSpec software and different iterative sine-wave fittings) and several checks performed (splitting of the timeseries in different subsets, investigation of the residual light curves and spectra. A level of 10^-5^mag was reached in the amplitude spectra of the CoRoT timeseries. The space monitoring was complemented by ground-based high-resolution spectroscopy, which allowed the mode identification of 30 terms. The frequency analysis of the CoRoT timeseries revealed hundreds of terms in the frequency range 0-30d^-1^. All the cross-checks confirmed this new result. The initial guess that delta Sct stars have a very rich frequency content is confirmed. The spectroscopic mode identification gives theoretical support since very high-degree modes (up to ell=14) are identified. We also prove that cancellation effects are not sufficient in removing the flux variations associated to these modes at the noise level of the CoRoT measurements. The ground-based observations indicate that HD 50844 is an evolved star that is slightly underabundant in heavy elements, located on the Terminal Age Main Sequence. Probably due to this unfavourable evolutionary status, no clear regular distribution is observed in the frequency set. The predominant term f1=6.92d^-1^ has been identified as the fundamental radial mode combining ground-based photometric and spectroscopic data. The CoRoT scientific programme contains other delta Sct stars, with different evolutionary statuses. The very rich and dense frequency spectrum discovered in the light curve of HD 50844 is the starting point for future investigations.