We report first-principles full potential linearised augmented plane wave calculations of the electronic band structure of the compound MgB2C2 and its hole-doped derivatives Mg0.5Li0.5B2C2, Mg0.5Na0.5B2C2, Mg0.9Na0.1B2C2 and Mg0.5K0.5B2C2. The parent compound MgB2C2 is a band insulator, which on hole doping, is predicted to turn metallic with a large density of states at the Fermi energy. Its band dispersion shows a flat band feature close to the Fermi energy, reminiscent of MgB2. Based on our estimates of changes in the density of states at the Fermi level, we predict that hole-doped MgB2C2 is a potential candidate for high-temperature superconductivity.