  We have measured the Raman spectra of polycrystalline MgB$_{2}$ from 25 {\cm}
to 1200 {\cm}. When the temperature was decreased below the superconducting
transition temperature $T_c$, we observed a superconductivity-induced
redistribution in the electronic Raman continuum. Two pair-breaking peaks
appear in the spectra, suggesting the presence of two superconducting gaps.
Furthermore, we have analyzed the measured spectra using a quasi
two-dimensional model in which two s-wave superconducting gaps open on two
sheets of Fermi surface. For the gap values we have obtained $\Delta_1 = 22
cm^{-1}$ (2.7 meV) and $\Delta_2 = 50 cm^{-1}$ (6.2 meV). Our results suggest
that a conventional phonon-mediated pairing mechanism occurs in the planar
boron $\sigma$ bands and is responsible for the superconductivity of MgB$_{2}$.
