The present invention relates to a composition for dyeing keratin fibers, comprising at least one fatty substance at least one surfactant at least one dye for keratin fibers, having a log P greater than or equal to 1.3 at least one alkaline agent at least one chemical oxidizing agent at least 0.5% by weight relative to the weight of the composition of at least one liquid non-ionic compound having a Hansen parameter δ H below 16 MPa ½ the fatty substance content representing in total at least 25% by weight relative to the total weight of the composition. The present invention also relates to a method using this composition, and to multi-compartment devices that are suitable for using this invention.
