We examine the transfer of electronic excitation (an exciton) along a chain of electronically coupled monomers possessing internal vibronic structure and which also interact with degrees of freedom of the surrounding environment. Using a combination of analytical and numerical methods, we calculate the time evolution operator or time-dependent Green's function of the system and thereby isolate the physical parameters influencing the electronic excitation transport. Quite generally, we show that coupling to vibrations slows down and inhibits migration of electronic excitation due to dephasing effects on the coherent transfer present without vibrations. In particular, coupling to a continuous spectrum of environment states leads to a complete halting of transfer, i.e., a trapping of the exciton.