A rotor for a helicopter, having: a hub rotating about an axis and in turn having a number of blades; and an at least partly hollow drive shaft connectable to a drive of the helicopter and connected functionally to the hub to rotate the hub about the axis; the rotor also having vibration damping means in turn having a mass, and an elastically deformable member connected to the mass and supported by the shaft; the member extending at least partly inside the shaft, and being elongated parallel to the axis; and the mass vibrating, in use, at such a frequency as to oppose transmission to the shaft of the vibration produced by rotation of the hub and blades.