The specific heat of the recently discovered superconductor MgB₂ has been measured at temperatures ranging from 4.5 to 80 K. The superconducting anomaly ΔC at T_c is clearly observed. The total specific heat in the normal state can be well fitted by electronic and phonon contributions. The Debye temperature θ_D is found to be 737 K, much larger than other intermetallic superconductors. The normal-state electronic specific heat coefficient γ is found to be 2.48±0.5 mJ/mol·K² and ΔC/γT_c is between 1.41 and 2.15.