We demonstrate monolithic aluminum gallium arsenide (AlGaAs) optical anoantennas. Using a selective oxidation technique, we fabricate such epitaxial semiconductor nanoparticles on an aluminum oxide substrate. Second harmonic generation from an AlGaAs nanocylinder of height h=400 nm 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 otpimized geometry.