We analyze dynamical heterogeneities in a simulated "bead-spring" model of a nonentangled, supercooled polymer melt. We explore the importance of chain connectivity on the spatially heterogeneous motion of the monomers. We find that when monomers move, they tend to follow each other in one-dimensional paths, forming strings as previously reported in atomic liquids and colloidal suspensions. The mean string length is largest at a time close to the peak time of the mean cluster size of mobile monomers. This maximum string length increases, roughly in an exponential fashion, on cooling toward the critical temperature T-MCT of the mode-coupling theory, but generally remains small, although large strings involving ten or more monomers are observed. An important contribution to this replacement comes from directly bonded neighbors in the chain. However, mobility is not concentrated along the backbone of the chains. Thus, a relaxation mechanism in which neighboring mobile monomers along the chain move predominantly along the backbone of the chains, seems unlikely for the system studied. (C) 2003 American Institute of Physics.