Being chased
Psychological (Freud)
Being chased usually shows the dreamer fleeing from something that lives within: a fear, a drive, or an unresolved conflict. The pursuer is often a split-off part of the self one refuses to look at, which is precisely why it gives chase.
Oriental reading
In traditional interpretation, being chased points to an enemy, a worry, or a hardship in waking life. Escaping or turning to face the pursuer is held by many to signal that one wards off harm and gains the upper hand.
Death & Danger
Dream interpretation is for self-reflection and entertainment — it is not a medical or psychological diagnosis.