Ternary rare-earth cobalt gallides RE4Co3Ga16 (RE = Gd–Er, Y) have been prepared by arc-melting of the elements followed by annealing at 800 °C. Single crystals of the Gd and Tb members were also grown in the presence of a Ga self-flux. They extend the rare-earth substitution possible in the Sm4Co3Ga16-type structure (Pearson symbol tP23, space group P4/mmm, Z = 1), in which additional Co atoms enter as self-interstitials into the parent RE2CoGa8 structure. Structural refinements were carried out on single-crystal (RE = Gd, Tb) and powder (RE = Dy, Ho, Er, Y) X-ray diffraction data. Cell parameters lie in the ranges of a = 6.03–5.96 Å and c = 11.11–10.96 Å. Magnetic measurements on RE4Co3Ga16 (RE = Gd, Tb, Dy) reveal that they order antiferromagnetically below TN of 19, 25, and 14 K, respectively; Y4Co3Ga16 is Pauli paramagnetic. The electrical resistivity of Tb4Co3Ga16 undergoes a transition coincident with the magnetic ordering temperature. Band structure calculations on Y4Co3Ga16 indicate that the major bonding contributions arise from Co–Ga and Ga–Ga interactions, with the stuffing of interstitial Co atoms into octahedral sites of the parent Y2CoGa8 structure, which provides additional Co–Ga bonding stabilization.