To dream that you are being chased signifies that you are avoiding a situation that you do not think is conquerable. It is 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.

To dream that you are chasing someone signifies that you are attempting to overcome a difficult goal or task. You may also be expressing some aggressive feelings toward others.

To dream that you are being chased and enjoying it implies that you like being the object of desire. You like feeling wanted. The dream may be analogous to a blossoming relationship.

For an in depth analysis, seeĀ Common Dreams: Chase.