Single crystals of LiCoO2 and LiNiO2 have been successfully grown for the first time by a flux method. A single-crystal X-ray diffraction study confirmed trigonal symmetry, and their lattice parameters were a = 2.8161(5) Angstrom and c = 14.0536(5) Angstrom for LiCoO2, and a = 2.8899(13) Angstrom and c = 14.1938(17) Angstrom for LiNiO2, respectively. The cation distribution in Li0.92Ni1.08O2 was determined to be (Li0.74Ni0.26)(3a)[Li0.18Ni0.82](3b)O-2 with a final R value of 2.7% by a single-crystal X-ray structure analysis. LiCoO2 proved to show a semiconducting behavior below room temperature by an in-plane electrical resistivity measurement using the single crystal specimen.