Boron hydride clusters are an extremely diverse compound class, which are of enormous importance to many areas of chemistry. Despite this, stable aluminium hydride analogues of these species have remained staunchly elusive to synthetic chemists. Here, we report that reductions of an amidinato-aluminium(III) hydride complex with magnesium(I) dimers lead to unprecedented examples of stable aluminium(I) hydride complexes, [(ArNacnac)Mg]2[Al6H6(Fiso)2] (ArNacnac = [HC(MeCNAr)2]−, Ar = C6H2Me3-2,4,6 Mes; C6H3Et2-2,6 Dep or C6H3Me2-2,6 Xyl; Fiso = [HC(NDip)2]−, Dip = C6H3Pri 2-2,6), which crystallographic and computational studies show to possess near neutral, octahedral hypercloso-hexaalane, Al6H6, cluster cores. The electronically delocalised skeletal bonding in these species is compared to that in the classical borane, [B6H6]2−. Thus, the chemistry of classical polyhedral boranes is extended to stable aluminium hydride clusters for the first time.