We report the covalent layer-by-layer construction of polyelectrolyte multilayer (PEM) films by using an efficient electrochemically triggered Sharpless click reaction. The click reaction is catalyzed by Cu(I) which is generated in situ from Cu(II) (originating from the dissolution of CuSO(4)) at the electrode constituting the substrate of the film. The film buildup can be controlled by the application of a mild potential inducing the reduction of Cu(II) to Cu(I) in the absence of any reducing agent or any ligand. The experiments were carried out in an electrochemical quartz crystal microbalance cell which allows both to apply a controlled potential on a gold electrode and to follow the mass deposited on the electrode through the quartz crystal microbalance. Poly(acrylic acid) (PAA) modified with either alkyne (PAA(Alk)) or azide (PAA(Az)) functions grafted onto the PAA backbone through ethylene glycol arms were used to build the PEM films. Construction takes place on gold electrodes whose potentials are more negative than a critical value, which lies between -70 and -150 mV vs Ag/AgCl (KCl sat.) reference electrode. The film thickness increment per bilayer appears independent of the applied voltage as long as it is more negative than the critical potential, but it depends upon Cu(II) and polyelectrolyte concentrations in solution and upon the reduction time of Cu(II) during each deposition step. An increase of any of these latter parameters leads to an increase of the mass deposited per layer. For given buildup conditions, the construction levels off after a given number of deposition steps which increases with the Cu(II) concentration and/or the Cu(II) reduction time. A model based on the diffusion of Cu(II) and Cu(I) ions through the film and the dynamics of the polyelectrolyte anchoring on the film, during the reduction period of Cu(II), is proposed to explain the major buildup features.