Context. Massive stars burn hydrogen through the CNO cycle during most of their evolution. When mixing is efficient or when mass transfer in binary systems occurs, chemically processed material is observed at the surface of O and B stars. Aims: ON stars show stronger lines of nitrogen than morphologically normal counterparts. Whether this corresponds to the presence of material processed through the CNO cycle is not known. Our goal is to answer this question. Methods: We performed a spectroscopic analysis of a sample of ON stars with atmosphere models. We determined the fundamental parameters as well as the He, C, N, and O surface abundances. We also measured the projected rotational velocities. We compared the properties of the ON stars to those of normal O stars. Results: We show that ON stars are usually rich in helium. Their CNO surface abundances are fully consistent with predictions of nucleosynthesis. ON stars are more chemically evolved and rotate - on average - faster than normal O stars. Evolutionary models including rotation cannot account for the extreme enrichment observed among ON main sequence stars. Some ON stars are members of binary systems, but others are single stars as indicated by stable radial velocities. Mass transfer is therefore not a simple explanation for the observed chemical properties. Conclusions: We conclude that ON stars show extreme chemical enrichment at their surface, consistent with nucleosynthesis through the CNO cycle. Its origin is not clear at present. Based on observations obtained 1) at the Anglo-Australian Telescope; 2) at the Canada-France-Hawaii Telescope (CFHT), which is operated by the National Research Council (NRC) of Canada, the Institut National des Science de l'Univers of the Centre National de la Recherche Scientifique (CNRS) of France, and the University of Hawaii; 3) at the ESO/La Silla Observatory under programs 081.D-2008, 083.D-0589, 086.D-0997; 4) the Nordic Optical Telescope, operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias; 5) the Mercator Telescope, operated on the island of La Palma by the Flemish Community at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias.Appendices are available in electronic form at http://www.aanda.orgThe reduced spectra are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/578/A109