The present invention relates to a composition for dyeing keratin fibres, and in particular human keratin fibres such as the hair, containing, in a support that is suitable for dyeing, at least one oxidation dye precursor, characterized in that it comprises at least one alcohol oxidase enzyme and at least one substrate for the said enzyme. This patent application also relates to a process for dyeing keratin fibres, which consists in applying this composition, and also to a dyeing "kit".