We report the realization of a high mobility [&mgr;&bartil;4.8×105cm2/(V s)] selectively doped GaAs/AlxGa1−xAs multiple quantum well structure with low density (ns&bartil;1.7×1011cm−2for each of the 85 wells) grown by molecular beam epitaxy. The activation energy for the fractional quantum Hall state at the Landau‐level filling factor &ngr;=1/3 is &Dgr;&bartil;2 K, the highest value ever reported for any multiple quantum well structure. Such a structure is nearly ideal for studies of the thermal properties of the two‐dimensional electron system in the fractional quantum Hall regime.