The title compound was detected and characterized during a systematic study of the Al-rich part of the Co-Al-Si system. The crystal structure was established via single-crystal X-ray diffraction. It represents a new type of structure of intermetallic compounds (Pearson symbol mC26, space group C2/m). The homogeneity range of the phase Co4Al7+xSi2-x (0.27(3) <= x <= 1.05(2)) and equilibria with neighboring phases were studied by electron probe microanalysis (EPMA) and X-ray powder diffraction. The lattice parameters of the compound were found to vary between Al-poor and Al-rich composition (a = 11,949(1)-12.042(1) angstrom, b = 3.9986(4)-4.0186(4) angstrom, c = 7.6596(8)-7.6637(9) angstrom, and beta = 106.581(7)-106.140(7)degrees). A partial disorder caused by the Al/Si substitution in one of the five main group element positions was found, and different ordering models yielding different Al/Si occupation motifs and different distributions of interatomic distances are discussed in detail. Chemical bonding analysis with the electron localization function (ELF) reveals a covalently bonded Al/Si network and rather ionic interactions between Co and the network.