We report the largest-size thin films of uniform single-layer MoS2 on sapphire substrates grown by chemical vapor deposition based on the reaction of gaseous MoO3 and S evaporated from solid sources. The as-grown thin films of single-layer MoS2 were continuous and uniform in thickness for more than 4 cm without the existence of triangular-shaped MoS2 clusters. Compared to mechanically exfoliated crystals, the as-grown single-layer MoS2 thin films possessed consistent chemical valence states and crystal structure along with strong photoluminescence emission and optical absorbance at high energy. These results demonstrate that it is possible to scale up the growth of uniform single-layer MoS2 thin films, providing potentially important implications on realizing high-performance MoS2 devices.