We study the neutral and charged optical excitations (excitons and trion) in the prototypical wide-gap insulator LiF using the first-principles GW/BSE approach and its extension for trions. In addition to neutral excitons we find bound trion states with a trion binding energy of 20-30 meV. At the same time the lowest bright exciton and trion are well separated by about 400 meV in the absorption spectrum both for the bulk and the (001) surface crystal. Even though the charged trions are slightly more extended compared to their neutral counterparts, they remain localized on a few atoms only and keep the Frenkel-like character of the neutral excitons. With such strongly localized trions, LiF stands out from currently investigated trionic materials and highlights itself for further studies.