If you dream someone is chasing you, consider the context.
If the chaser wants to harm you, this can represent a feeling or fear of: persecution, hostility, aggression, criticism, etc. by another person or by "people in general." It can also represent real-life situation where you feel your boundaries have been crossed or your integrity has been compromised.
If someone who likes you is playfully chasing you, it could represent your perception that they like you or might want to know you better.