Parametric optics and second harmonic generation in pure plasmonic particle chains are studied. By a proper design of the plasmonic particle geometry, the modes supported by the chain can achieve phasematching conditions. Then the magnetic-field dependence of the plasmon electric susceptibility can provide the nonlinearity and the coupling mechanism leading to parametric processes, sum frequency and second harmonic generation. Hence, chains of plasmonic particles can support parametric optics and higher harmonic generation by using its own modes only. Since the second order nonlinearity involves both electric and magnetic fields, the SHG reported here is supported also by centrosymmetric particle chains.