We report the first experimental study of sub-Doppler cooling in alkaline earth atoms (87Sr) enabled by the presence of nuclear spin-originated magnetic degeneracy in the atomic ground state. Sub-Doppler cooling in a sigma(+)-sigma(-) configuration is achieved despite the presence of multiple, closely spaced excited states. This surprising result is confirmed by an expanded multilevel theory of the radiative cooling force. Detailed investigations of system performance have shed new insights into (sigma(+)-sigma(-)) cooling dynamics and will likely play an important role in the future development of neutral atom-based optical frequency standards.