We have studied the glass transition dynamics of trans-1,4-chloroprene from microscopic view points using a quasielastic neutron scattering technique In a time range of similar to 4 x 10(-13) to similar to 4 x 10(-10) s. It was found that the so-called fast process of picosecond order appears at around the Vogel-Fulcher temperature To, similarly to cis-1,4-polybutadiene having no large side groups [J. Chern. Phys. 98, 8262 (1993)]. It is considered that the onset temperature at around To must be characteristic to polymers having no large side groups or no large internal degrees of freedom. In addition to the fast process, the slow process of; subnanosecond order sees in at around the glass transition temperature T-g and the activation energy of the relaxation time was found to be similar to 2.5 kcal/mol. The nature of the slow process is discussed in terms of conformational transition near T-g.