We present the first evidence of vitrification of a single-component monatomic liquid in two dimensions, where atoms interact isotropically through the Lennard-Jones-Gauss potential [M. Engel and H.-R. Trebin, Phys. Rev. Lett. 98, 225505 (2007)]. With the use of a molecular dynamics simulation, we quench the system from a melt to a state well below the melting temperature. At lower temperatures, the state of this system does not have any long range order nor show any structural relaxation. We obtain various physical quantities such as the specific heat, the intermediate scattering function and the mean square displacement during the cooling process and demonstrate that the structural relaxation of the monatomic liquid shows characteristic behaviors of the common glass transition.