Dreaming of being chased is sign of something bad in future as per dream meaning and interpretation. You need to avoid arguments and taking risk. You should not get into fights with people. You should control your anger and have patience.
Dream of being chased by strangers means accident or you might unintentionally hurt someone. You might be mistaken for someone else.
Dream of being chased by people you know is problems in relationship. You might suddenly feel someone you trusted is cheating. You might find out about someone working against you.
Dreaming of being chased and you are happy means meeting with friends or vacation.