(1) If you are being chased in a dream, what is chasing you probably symbolizes something you are afraid of, either in your external life or - more commonly - in your inner self, your unconscious. For example, a woman who dreams of being chased by men is probably afraid of sex. (Freud would add that her dreams present, in disguise, an unconscious, repressed desire for sex.)
(2) If you are doing the chasing, the ‘you’ in your dream is probably your conscious ego and the thing you are chasing is almost certainly some part of yourself that frightens you. Chasing it away means disowning it, banishing it from your conscious life. It might be much better to try to integrate it into your conscious life. At the very least, get to know it and understand it.
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