In a method for supplying nitrogen to a combustion chamber, gaseous nitrogen (9) is drawn off from an air separation unit (7) at a first pressure, the nitrogen is compressed in at least two stages (C1, C2) of a nitrogen compressor and sent to a combustion chamber (25) at a second pressure, which is the output pressure of the last stage (C3) of the nitrogen compressor, between two stages of the nitrogen compressor the nitrogen is humidified by direct contact in passing through a contactor (17) supplied at its top with water, and the humidified nitrogen is compressed in at least one stage of the nitrogen compressor and sent to the combustion chamber.