This note presents a feasibility study of the search for a new heavy charged gauge boson with the CMS detector at the Large Hadron Collider LHC. The model assumes the existence of a heavy carbon copy of the Standard Model W (Reference Model by Altarelli) generically denoted as Wprime. Such a boson has been investigated in the decay channel Wprime --> \mu \nu using the full detector simulation including minimum bias events (pile-up) according to the expected first years of luminosity. All relevant Standard Model backgrounds have been considered. Such a new boson is expected to be discovered, if existant, with a mass of 0.1-4.6 TeV for an integrated luminosity of 10 fb^-1. The range can be expanded to 6.1 TeV with an integrated luminosity of 300 fb^-1. If no signs for a Wprime boson appear 95% CL exclusion limits of 4.7 TeV and 6.2 TeV can be set respectively
