The electronic structure and chemical bonding in the ternary transition metal bismuthides Ti4TBi2 (T = Cr, Mn, Fe, Co, and Ni) is investigated by approximate MO calculations of the extended Huckel tight-binding type. These intermetallic compounds crystallize in a layer structure, repeating sequence T-Ti/Bi-T-Ti/Bi, stacking along c; the late transition metals form linear chains with short T-T bonds. Other important structural elements are face-sharing chains of Ti4Bi2 octahedra and Bi channels. The decrease of the T-T bond lengths from Cr to Ni is more pronounced than expected from the decrease of the metallic radii alone. The analysis of the electronic structure indicates that this behavior arises from the titanium-titanium and titanium-bismuth interlayer interactions. Diminution of the titanium-titanium interlayer distances as one goes from Ti4CrBi2 to Ti4NiBi2 is due to Ti(d)-Ti(d) bonding, which increases with increasing electron filling of the titanium d levels. The titanium-bismuth interactions remain strong along this series, as can also be seen by the constant intralayer/titanium-bismuth distances. A distinguishing feature of the title compounds is the channels formed by bismuth atoms. These channels are filled by Bi-centered, essentially unhybridized 6p orbitals forming a 2D net stacking along c and interacting with each other, stronger in the c direction than perpendicular to it. The possibility of intercalating electrophilic species into these electron-filled voids is also investigated.