Local chain dynamics of atactic polypropylene, a typical amorphous vinyl polymer, has been studied by both quasielastic neutron scattering and macroradical decay measurements by electron spin resonance to detect the fast process of picosecond order observed for most amorphous materials. It was found that the fast process sets in at the Vogel-Fulcher temperature T-0, similar to observations for other simple polymers, suggesting that the fast process is a precursor of the glass transition. In coincidence with the onset of the fast process, the acceleration of the macroradical decay is also observed in the vicinity of T-0, indicating a close connection of both phenomena. This is the first experimental evidence for the fast process from two independent measurements.