We demonstrate monolithic aluminum gallium arsenide (AlGaAs) optical nanoantennas. Using a selective oxidation technique, we fabricated epitaxial semiconductor nanocylinders on an aluminum oxide substrate. Second harmonic generation from AlGaAs nanocylinders of 400 nm height and varying radius pumped with femtosecond pulses delivered at 1554-nm wavelength has been measured, revealing a peak conversion efficiency exceeding 10-5 for nanocylinders with an optimized geometry.