If you are being chased, maybe you are running away from or trying to escape those things that are frightening and unpleasant (possibly your own habits and negative behaviors).
If you are doing the chasing, it may be that you are expressing some aggressive feelings toward others or are pursuing a very difficult goal. On the deepest level, if a stranger is chasing you it may represent your chasing a part of yourself, the unconscious attempts to catch up with the conscious in order for you to become more aware of yourself and your own multidimensional nature. [1]
If fear is involved in this experience then you must test all the signs and employ meditation to seek the answer. [3]
If the dreamer is the pursuer, he or she may be chasing after a difficult goal. [4]
If the enemy catches you, the portent is one of failure. [5]
chased, being: running from a frightening situation.
by opposite sex: are denying your own sexual drive.
shadowy creature: an early trauma is trying to be reheard and solved.
chasing: an elopement wil cause much gossip; is that goal real y yours? [7]