The growth of large area single-layer graphene (1-LG) is studied using ambient pressure chemical vapor deposition on single-crystal Ni(111), Ni(110), and Ni(100). By varying both the furnace temperature in the range of 800-1100 degrees C and the gas flow through the growth chamber, uniform, high-quality 1-LG is obtained for Ni(111) and Ni(110) single crystals and for Ni(100) thin films. Surprisingly, only multilayer graphene growth could be obtained for single-crystal Ni(100). The experimental results are analyzed to determine the optimum combination of temperature and gas flow. Characterization with optical microscopy, Raman spectroscopy, and optical transmission support our findings. Density-functional theory calculations are performed to determine the energy barriers for diffusion, segregation, and adsorption, and model the kinetic pathways for formation of different carbon structures on the low-index surfaces of Ni.