Context. Although still beyond our observational abilities, Population III stars are interesting objects from many perspectives. They are responsible for the re-ionisation of the inter-galactic medium. They also left their chemical imprint in the early Universe, which can be deciphered in the most metal-poor stars in the halo of our Galaxy. Aims. Rotation has been shown to play a determinant role at very low metallicity, bringing heavy mass loss where almost none was expected. Is this still true when the metallicity strictly equals zero? The aim of our study is to answer this question, and to determine how rotation changes the evolution and the chemical signature of the primordial stars. Methods. We have calculated seven differentially-rotating stellar models at zero metallicity, with masses between 9 and 200 M⊙. For each mass, we also calculated a corresponding model without rotation. The evolution is followed up to the pre-supernova stage. Results. We find that Z = 0 models rotate with an internal profile Ω(r) close to local angular momentum conservation, because of a very weak core-envelope coupling. Rotational mixing drives an H-shell boost due to a sudden onset of the CNO cycle in the shell. This boost leads to a high 14N production, which can be asmuch as 106 times higher than the production of the non-rotating models. Generally, the rotating models produce much more metal than their non-rotating counterparts. The mass loss is very low, even for the models that reach critical velocity during the main sequence. It may however have an impact on the chemical enrichment of the Universe, because some of the stars are supposed to collapse directly into black holes. They would contribute to the enrichment only through their winds. While in that case non-rotating stars would not contribute at all, rotating stars may leave an imprint on their surrounding. Due to the low mass loss and the weak coupling, the core retains a high angular momentum at the end of the evolution. The high rotation rate at death probably leads to a much stronger explosion than previously expected, changing the fate of the models. The inclusion of our yields in a chemical evolution model of the Galactic halo predicts log values of N/O, C/O and 12C/13C ratios of –2.2, –0.95 and 50 respectively at logO/H +12 = 4.2.