A new ternary aluminide, LaNi1+xAl6-x (X = 0.44), has been synthesized from La, Ni, and Al in sealed silica tubes. Its structure, determined by single-crystal X-ray diffraction, is tetragonal P4/mmm (No. 123) with Z = 1 and has the lattice parameters a = 4.200(8) and c = 8.080(8) Angstrom. Refinement based on F-o(2) yielded R-1 = 0.0197 and wR(2) = 0.020 [l > 2 sigma(l)]. The compound adopts a structure type previously observed in SrAu2Ga5 and EuAu2Ga5. The atomic arrangement is closely related to the one in BaAl4 as well as in other rare-earth gallide compounds such as LaNi0.6Ga6, HoCoGa5, Ce4Ni2Ga20, Ce4Ni2Ga17, Ce4NiGa18, and Ce3Ni2Ga15. This structure exhibits a large open cavity which may be filled by a guest atom. Band structure calculations using density functional theory have been carried out to understand the stability of this new compound.