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He's always chasing girls.

The shopkeeper was tired of chasing his debtors so from then on he demanded payment in full.

Pac-Man, when a certain condition is reached, can counter attack and eat the monsters chasing him.

My little sister and I used to play tag a lot. We would chase each other, and the one chasing would try to tag the one being chased and yell: "You're it!"

You're beautiful and intelligent, how is it possible that no man is chasing after you?