The (4) over bar crystal symmetry in materials such as GaAs can enable quasi-phasematching for efficient optical frequency conversion without poling, twinning or other engineered domain inversions. (4) over bar symmetry means that a 90 degrees rotation is equivalent to a crystallographic inversion. Therefore, when light circulates about the (4) over bar axis, as in GaAs whispering-gallery-mode microdisks, it encounters effective domain inversions that can produce quasi-phasematching. Microdisk resonators also offer resonant field enhancement, resulting in highly efficient frequency conversion in micrometre-scale volumes. These devices can be integrated in photonic circuits as compact frequency convertors, sources of radiation or entangled photons. Here we present the first experimental observation of second-harmonic generation in a whispering-gallery-mode microcavity utilizing (4) over bar -quasi-phasematching. We use a tapered fibre to couple into the 5-mu m diameter microdisk resonator, resulting in a normalized conversion efficiency eta approximate to 5 x 10(-5) mW(-1). Simulations indicate that when accounting for fibre-cavity scattering, the normalized conversion efficiency is eta approximate to 3 x 10(-3) mW(-1).