Natural bacterial populations are subjected to constant predation pressure by bacteriophages. Bacteria use a variety of molecular mechanisms to defend themselves from phage predation. However, since phages are nonmotile, perhaps the simplest defense against phage is for bacteria to move faster than phages. In particular, chemotaxis, the active migration of bacteria up attractant gradients, may help the bacteria escape slowly diffusing phages. Here we study phage infection dynamics in migrating bacterial populations driven by chemotaxis through low viscosity agar plates. We find that expanding phage–bacteria populations supports two moving fronts, an outermost bacterial front driven by nutrient uptake and chemotaxis and an inner phage front at which the bacterial population collapses due to phage predation. We show that with increasing adsorption rate and initial phage population, the speed of the moving phage front increases, eventually overtaking the bacterial front and driving the system across a transition from a regime where bacterial front speed exceeds that of the phage front to one where bacteria must evolve phage resistance to survive. Our data support the claim that this process requires phage to hitchhike with moving bacteria. A deterministic model recapitulates the transition under the assumption that phage virulence declines with host growth rate which we confirm experimentally. Finally, near the transition between regimes we observe macroscopic fluctuations in bacterial densities at the phage front. Our work opens a new, spatio-temporal, line of investigation into the eco-evolutionary struggle between bacteria and phage.