Exposure of tetrabutylammonium aluminium hydride to 60Co γ-rays at 77 K gave two species exhibiting large, nearly isotropic, hyperfine coupling to 27Al. One species, similar to that previously thought to be ·AlH–3 in irradiated lithium aluminium hydride, is now assigned to a hydroxylated impurity anion. The other, which exhibited hyperfine coupling to three equivalent protons, is clearly authentic ·AlH–3. This species was rotating in the solid matrix at 77 K, but anisotropic parameters were extracted from the spectra at 4 K. The results confirm the pyramidal character of ·AlH–3, but the estimated 3s population of 15.6% is almost equal to that for the isoelectronic radical ·SiH3(15.0%)(P. J. Krusic and J. K. Kochi, J. Am. Chem. Soc., 1969, 91, 3938; S. W. Bennett, C. Eaborn, A. Hudson, R. A. Jackson and K. D. J. Root, J. Chem. Soc. A, 1970, 348) rather than being greater, as had been previously postulated.