The correct functioning of cells requires the orchestration of multiple cellular processes, many of which are inherently dynamical. The conditions under which these dynamical processes entrain each other remain unclear. Here we use synthetic biology to address this question in the case of concurrent cellular oscillations. Specifically, we study at the single-cell level the interaction between the cell division cycle and a robust synthetic gene oscillator in Escherichia coli. Our results suggest that cell division is able to partially entrain the synthetic oscillations under normal growth conditions, by driving the periodic replication of the genes involved in the oscillator. Coupling the synthetic oscillations back into the cell cycle via the expression of a key regulator of chromosome replication increases the synchronization between the two periodic processes. A simple computational model allows us to confirm this effect.