Normal mode splitting is observed in a cavity QED system, in which nitrogen vacancy centers in diamond nanocrystals are coupled to whispering gallery modes in a silica microsphere. The composite nanocrystal-microsphere system takes advantage of the exceptional spin properties of nitrogen vacancy centers as well as the ultra high quality factor of silica microspheres. The observation of the normal mode splitting indicates that the dipole optical interaction between the relevant nitrogen vacancy center and whispering gallery mode has reached the strong coupling regime of cavity QED.