Modulation‐doped GaAs heterostructures with low‐temperature electron mobilities of 5.0×106cm2/V s at a two‐dimensional electron areal density of 1.6×1011cm−2have been made. The mobilities are the highest ever observed in a semiconductor. Multiple quantum wells of GaAs prepared by similar methods showed electron mobilities up to 0.54×106cm2/V s at an areal density of 5.3×1011cm−2per layer, which also exceeds any mobility value previously reported for multiple well structures. The structures were grown by molecular beam epitaxy with an atomic‐plane sheet‐doping technique.