  In this paper, we study a new micro-macro model for a reactive polymeric
fluid, which is derived recently in [Y. Wang, T.-F. Zhang, and C. Liu, \emph{J.
Non-Newton. Fluid Mech.} 293 (2021), 104559, 13 pp], by using the energetic
variational approach. The model couples the breaking/reforming reaction scheme
of the microscopic polymers with other mechanical effects in usual viscoelastic
complex fluids. We establish the global existence of classical solutions near
the global equilibrium, in which the treatment on the chemo-mechanical coupling
effect is the most crucial part. In particular, a weighted Poincar\'e
inequality with a mean value is employed to overcome the difficulty that arises
from the non-conservative number density distribution of each species.
