  Measurements of the specific heat of Mg ^{11}B_2 (MgB2), from 1 to 50 K, in
magnetic fields to 9 T, give the Debye temperature, $\Theta$ = 1050 K, the
coefficient of the normal-state electron contribution, $\gamma_n$ = 2.6 mJ
mol^{-1} K^{-2}, and a discontinuity in the zero-field specific heat of 133 mJ
mol^{-1} K^{-1} at $T_c$ = 38.7 K. The estimated value of the electron-phonon
coupling parameter, $\lambda$ = 0.62, could account for the observed $T_c$ only
if the important phonon frequencies are unusually high relative to $\Theta$. At
low $T$, there is a strongly field-dependent feature that suggests the
existence of a second energy gap, about four times smaller than the major gap.
