By performing a swarm-intelligent global structure search combined with first-principles calculations, a stable two-dimensional (2D) AlB3 heterostructure with directed, covalent Al-B bonds forms due to a nearly perfect lattice match between 2D borophene and the Al(111) surface. The AlB3 heterosheet with the P6mm space group is composed of a planar Al(111) layer and a corrugated borophene layer, where the in-plane coordinates of Al covalently link with the corrugated B atoms. The resulting structure shows a similar interlayer interaction energy to that of the Al(111) surface layer to the bulk and high mechanical and thermal stability, possesses multiple Dirac points in the Brillouin zone with a remarkably high Fermi velocity of 1.09 × 106 m s-1, which is comparable to that of graphene. Detailed analysis of the electronic structure employing the electron localisation function and topological analysis of the electron density confirm the covalent Al-B bond with high electron localisation between the Al and B centres and with only little interatomic charge transfer. The combination of borophene with metal monolayers in 2D heterostructures opens the door to a rich chemistry with potentially unprecedented properties.