Optical second-harmonic generation (SHG) has been studied in a trimer smectic C* liquid crystal especially designed for nonlinear optical applications. The molecule has a long conjugated donor-acceptor unit that transversally links three parallel rod-shaped moieties. A strong SHG signal has been observed at a fundamental wavelength of 1369 nm even in the presence of the spontaneous helicoidal structure of the smectic C* phase. This unusual behavior has been interpreted as due to the existence of phase matching, in which the wave vector mismatch is compensated by the wave vector of the helix. This point has been confirmed by the study of the SHG intensity versus sample thickness and light polarization characteristics. The main coefficient of the second-order susceptibility tensor of the material has been estimated to be d(22) = 28 pm/V.