The sub-barrier fusion excitation functions are measured for the first time for the system ⁷Li ⁺²⁸Si by the characteristic γ -ray method in the energy range E_lab = 7–11.5 MeV. The results show an enhancement, below the barrier, by about a factor of two when compared with the one-dimensional barrier penetration (1D BPM) model. Introduction of coupling with the rotational 2⁺ state (1.779 MeV) of the target improves the fit somewhat, but still an enhancement of about 25–40% remains.