The chase sequence is always a dramatic part of a story. Will the bad guy get away? Will the heroes manage to catch him?
Good games will have mechanics designed to carry across the excitement of a chase into the game play. Nothing is ever certain, because obstacles or tactics can mean a slower quarry can evade the pursuers, while circumstances or clever planning may allow slower pursuers to intercept a faster fugitive. And chases frequently lead to mayhem and collateral damage as bystanders get in the way and bits of scenery go flying.
And that's all before you add in the complications of a group of players being in charge of one of the chase parties.
GM: Padmé, Anakin, Obi-Wan: Make a Spot check.
Obi-Wan: I rolled highest. 15.
GM: You see Count Dookû speeding away into the desert on a hoverbike.
Padmé: After him!
Anakin: A war zone is no place for a Senator. We have to get you to safety.
Obi-Wan: He's leaving the battlefield anyway. We can intercept him.
Anakin: Not with the Senator. What sort of desert is this?
GM: Sand dunes.
Anakin: I push Padmé out of the ship.
Anakin: I use Force Levitation to make sure she's unhurt. We'll pick her up when Dookû's dealt with.
GM: Er... you land in the loose, gritty sand.
Padmé: At least I'm not a robot.
R2-D2: Does nothing upset you??