A cooled turbine rotor blade for a gas turbine engine is provided. The engine has an annular flow path for conducting working fluid though the engine. The blade has an aerofoil section for extending across the annular flow path. The blade further has a root portion radially inward of the aerofoil section for joining the blade to a rotor disc of the engine. The blade further has a platform between the aerofoil section and the root portion. The platform extends laterally relative to the radial direction of the engine to form an inner boundary of the annular flow path and to provide a rear overhang portion which projects in use towards a corresponding platform of a downstream nozzle guide vane. The platform contains at least one internal elongate plenum chamber for receiving cooling air. The longitudinal axis of the plenum chamber is substantially aligned with the circumferential direction of the engine. The plenum chamber supplies the cooling air to a plurality of exit holes formed in the external surface of the rear overhang portion to cool that portion.