We use molecular simulation to analyze liquid dynamics in the vicinity of the liquid-liquid phase transition (LLPT) recently discovered in the modified embedded-atom model for elemental gallium. For this purpose we analyze the diffusive behavior in terms of the mean-squared displacement and self-intermediate scattering functions for two systems obtained by cooling the stable liquid through the LLPT at different cooling rates. The results show a pronounced heterogeneity of the dynamics upon the onset of the LLPT. Furthermore, it is found that this heterogeneity is closely correlated to the structural properties of the 9-fold coordinated high-density and 8-fold coordinated low-density liquid forms involved in the transition, showing a mixture of domains with very different diffusion time scales. The dynamics of the low-density liquid is found to be much more sluggish than that of the high-density form. Analysis of the energetics suggests that the origin of this difference is rooted in the fact that the cohesion in the former is significantly stronger than that in the latter.136064513