This letter describes high electron mobility transistors (HEMT's) utilizing a conducting channel which is a single In<inf>0.15</inf>Ga<inf>0.85</inf>AS quantum well grown pseudomorphically on a GaAs substrate. A Hall mobility of 40 000 cm<sup>2</sup>/V.s has been observed at 77 K. Shubnikov-de Haas oscillations have been observed at 4.2 K which verify the existence of a two-dimensional electron gas at the In<inf>0.15</inf>Ga<inf>0.85</inf>As/GaAs interface. HEMT's fabricated with 2-µm gate lengths show an extrinsic transconductance of 90 and 140 mS/mm at 300 and 77 K, respectively-significantly larger than that previously reported for strained-layer superlattice In<inf>x</inf>Ga<inf>1-x</inf>As structures which are nonpseudomorphic to GaAs substrates. HEMT's with 1-µm gate lengths have been fabricated, which show an extrinsic transconductance of 175 mS/mm at 300 K which is higher than previously reported values for both strained and unstrained In<inf>x</inf>Ga<inf>1-x</inf>As FET's. The absence of Al<inf>x</inf>Ga<inf>1-x</inf>As in these structures has eliminated both the persistent photoconductivity effect and drain current collapse at 77 K.