Transition metal carbides (TMCs) are a large family of materials with many intriguing properties and applications, and high-quality 2D TMCs are essential for investigating new physics and properties in the 2D limit. However, the 2D TMCs obtained so far are chemically functionalized, defective nanosheets having maximum lateral dimensions of similar to 10 mu m. Here we report the fabrication of large-area high-quality 2D ultrathin alpha-Mo2C crystals by chemical vapour deposition (CVD). The crystals are a few nanometres thick, over 100 mu m in size, and very stable under ambient conditions. They show 2D characteristics of superconducting transitions that are consistent with Berezinskii-Kosterlitz-Thouless behaviour and show strong anisotropy with magnetic field orientation; moreover, the superconductivity is also strongly dependent on the crystal thickness. Our versatile CVD process allows the fabrication of other high-quality 2D TMC crystals, such as ultrathin WC and TaC crystals, which further expand the large family of 2D materials.