The present invention relates to a composition for dyeing keratin fibres, in particular keratin fibres such as the hair, comprising: a) at least one oxidation base 3-(2,5-diaminophenyl)-1-propanol and/or acid salts thereof or solvates thereof such as hydrates; b) at least one coupler; c) at least 10% by weight relative to the total weight of the composition of a fatty substance which is preferably liquid and non-silicone-based; d) at least one saccharide thickening polymerp; e) optionally at least one basifying agent; and f) optionally at least one chemical oxidizing agent. The invention also relates to a process for dyeing keratin fibres such as the hair using the composition of the invention, and to a multi-compartment device for using the composition of the invention.