Dreaming that you are being chased means that you are avoiding a situation that you do not think is conquerable. It is often a metaphor for some form of insecurity. In particular, to dream that you are chased by an animal, represents your own unexpressed and unacknowledged anger which is being projected onto that animal. Alternatively, you may be running away from a primal urge or fear.  Dreaming that you are chasing someone means that you are attempting to overcome a difficult goal or task. You may also be expressing some aggressive feelings toward others.