Rotational studies at a variety of ages and masses are important for constraining the angular momentum evolution of young stellar objects (YSO). Of particular interest are the very low mass (VLM) stars and brown dwarfs (BDs), because of the significant lack of known rotational periods in that mass range. We aim to extend previous studies well down into the substellar regime, providing for the first time information on rotational periods for a large sample of young VLM stars and BDs. This extensive rotational period study of YSOs in the 1 Myr old Orion Nebula Cluster (ONC) is based on a deep photometric monitoring campaign using the Wide Field Imager (WFI) camera on the ESO/MPG 2.2m telescope on La Silla, Chile. Time series data was obtained with about 95 data points spread over 19 nights. Accurate I-band photometry of 2908 stars was obtained within a magnitude range of 13 to 21mag, i.e. extending three magnitudes deeper than previous studies in the ONC. Two different power spectral analysis techniques were used to search for periodic variability. In addition, the chi^2^ variability test was used for the detection of irregular variables.