[en] The elastic scattering of a secondary ¹¹Li beam (29 MeV/n) on a ²⁸Si target has been measured for the first time. To compensate for the low intensity of the secondary beam, an efficient detecting system permitting to obtain reliable experimental data has been used. An attempt has been made to reproduce the data in a phenomenological analysis and with coupled-channel calculations with a double folding optical potentials, with energy and density dependent effective interaction and realistic densities. In coupled-channel calculations with the folding optical potential a better description is achieved if a neutron halo of ¹¹Li is taken into account. (author) 30 refs.; 7 figs.; 4 tabs