Electro-oxidation of the quinoidal bisdithiazole BT in dichloroethane in the presence of [Bu4N][GaBr4] affords the 1:1 radical ion salt [BT][GaBr4], crystals of which belong to the trigonal space group P3. The packing pattern of the radical cations provides a rare example of an organic kagome basket structure, with S = 1/2 radical ion chains located at the triangular corners of a trihexagonal lattice. Magnetic measurements over a wide temperature range from 30 mK to 300 K suggest strongly frustrated AFM interactions on the scale of J/kb ∼ 30 K, but reveal no anomalies that would be associated with magnetic order. These observations are discussed in terms of the symmetry allowed magnetic interactions within and between the frustrated layers.