Crystalline samples of carbon-doped CaB4 were synthesized by solid-state reactions in sealed niobium ampules from the elements Ca, B, and C. The structure was determined by single-crystal X-ray diffraction (P4/mbm, Z = 4, a = 7,0989(7) angstrom, c = 4.1353(5) angstrom, R1 = 0.026, and wR2 = 0.058) revealing an atom arrangement containing a three-dimensional boron network built up from B-6 octahedra and B-2 dumbbells which is well-known from the structures of rare earth tetraborides. Crystals of CaB4-xCx are black with a metallic luster and behave stable against mineral acids. Band structure calculations indicate that CaB4 is a stable semiconducting compound with a narrow band gap and that carbon should not necessarily be required for the stability of this compound. The presence of carbon in the crystalline samples of CaB4-xCx was indicated by electron energy loss spectroscopy, but the carbon content in the samples was estimated to be less than 5% according to inductively coupled plasma-atomic emission spectrometry measurements. The distribution of boron and carbon atoms in the structure was investigated by means of B-11 and C-13 solid-state magic angle spinning NMR. Measurements of the magnetic susceptibility indicate a temperature-independent paramagnetism down to 20 K.