A new ternary, intermetallic compound, Ba14Zn5-xAl22+x, was synthesized by heating the pure elements at 900°C. This compound crystallizes in the monoclinic space group I2/m, Z=2, with a=10.474(2)Å, b=6.0834(14)Å, c=34.697(8)Å and β=90.814(4)°. The crystal structure of Ba14Zn5-xAl22+x consists of [Zn5-xAl22+x] slabs that are built with a novel, two-dimensional (2D) network of Zn and Al atoms involving eight-membered rings sandwiched between two layers of trigonal bipyramids interconnected by three-center bonding. Tight-binding, linear muffin-tin orbital (TB-LMTO-ASA) calculations have been performed to understand the relationship between composition and orbital interactions in the electronegative element framework. This new structure is closely related to the high-pressure, cubic Laves-type structure of BaAl2 as well as the ambient pressure binary compound, Ba7Al13. The degree of valence electron charge transfer from the electropositive Ba atoms is related to the Al:Ba molar ratio in the Ba-Zn-Al system.