An effect of optical-frequency current shot-noise suppression in a drifting charged particle beam and a corresponding process of particles self ordering are analyzed in a 3D model and verified by numerical simulations. The analysis confirms the single mode Langmuir plasma wave model of quarter wavelength longitudinal plasma oscillation, and defines the beam parameters regime for obtaining this effect. The control over relativistic beam shot noise can be utilized to avoid microbunching instabilities and to enhance the coherence of free electron lasers.