The Bedside Dream Dictionary

by Silvana Amar
Folklore interpretations say that if you are looking at a chase or participating in it, you will have a comfortable old age. Although this may be comforting, there is a more realistic understanding of this activity in a dream.

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.

Strangest Dream Explanations

by Dream Explanations - Anonymous
Dreams of chasing or of being chased signifies that you believe that what you need is out of reach, you are being seduced by the thrill of the hunt, or that you are running from an undesirable aspect of your self or from an adverse influence. Keep in mind that what you resist, persists.

Encyclopedia of Dreams

by Michael and Elizabeth Thiessen
If you see a chase in progress or if you participate in a chase you will look forward to a comfortable retirement and good health in your latter years.

If fear is involved in this experience then you must test all the signs and employ meditation to seek the answer.