A new mechanism of electron paramagnetic resonance in spherical zinc-blende semiconductor nanocrystals, based on the extended orbital motion of electrons in the entire nanocrystal, is presented. Quantum confinement plays a crucial role in making the resonance signal observable. The mechanism remains operative in nanocrystals with uniaxially distorted shape. A theoretical model based on the proposed mechanism is in good quantitative agreement with unusual ODMR spectra observed in nearly spherical CdSe nanocrystals.