We report the first realization of molecular beam epitaxy grown strained GaN quantum well field-effect transistors on single-crystal bulk AlN substrates. The fabricated double heterostructure FETs exhibit a two- dimensional electron gas (2DEG) density in excess of 2x10^13/cm2. Ohmic contacts to the 2DEG channel were formed by n+ GaN MBE regrowth process, with a contact resistance of 0.13 Ohm-mm. Raman spectroscopy using the quantum well as an optical marker reveals the strain in the quantum well, and strain relaxation in the regrown GaN contacts. A 65-nm-long rectangular-gate device showed a record high DC drain current drive of 2.0 A/mm and peak extrinsic transconductance of 250 mS/mm. Small-signal RF performance of the device achieved current gain cutoff frequency fT~120 GHz. The DC and RF performance demonstrate that bulk AlN substrates offer an attractive alternative platform for strained quantum well nitride transistors for future high-voltage and high-power microwave applications. ; Comment: 4 Pages, 4 Figures