Reported are the synthesis of three new Zintl phases, Ba2ZnAs2 (I), Ba2ZnSb2 (II), Ba2ZnBi2 (III) and their structural characterization by single-crystal X-ray diffraction. They are isoelectronic and isotypic and crystallize in the orthorhombic space group lbam, with four formula units per cell (Pearson symbol o/20; K2SiP2 type). Lattice parameters are as follows: a = 13.399(9)/14.133(3)114.325(6); b=6.878(5)/7.1919(15)/7.280(3); and c=6.541(4)/6.9597(15)/7.089(3) angstrom for I/II/III, respectively. The structure can be viewed as polyanionic chains, (1)(infinity)[ZnPn(2)](4-) (Pn = As, Sb, Bi), running parallel to the c-axis, with Ba2+ cations separating them. The chains are made of edge-shared ZnPn(4) tetrahedra, which are isosteric with the (1)(infinity)[SiS4/2] chains in SiS2. This and some other structural parallels with known Zintl phases have been discussed. The experimental results have been complemented by tight-binding linear muffin-tin orbital electronic structure calculations.