Collective cell migration in morphogenesis and cancer progression often involves the coordination of multiple cell types. How reciprocal interactions between adjacent cell populations lead to new emergent behaviours remains unknown. Here we studied the interaction between neural crest (NC) cells, a highly migratory cell population, and placodal cells, an epithelial tissue that contributes to sensory organs. We found that NC cells chase placodal cells by chemotaxis, and placodal cells run when contacted by NC. Chemotaxis to Sdf1 underlies the chase, and repulsion involving PCP and N-cadherin signalling is responsible for the run. This chase-and-run requires the generation of asymmetric forces, which depend on local inhibition of focal adhesions. The cell interactions described here are essential for correct NC migration and for segregation of placodes in vivo and are likely to represent a general mechanism of coordinated migration.