Chase Dreams
Chase dreams is one of several common dream themes. As with most of the common dreams, they often stem from feelings of anxiety in your waking life. Running is an instinctive response to physical threats in your environment. In these dreams, you can be pursued by an attacker, an animal or an unknown figure, who wants to hurt or possibly kill you. In turn, you run, hide or try to outwit your pursuer. Your actions in the dream parallel how you respond to pressure and cope with fears, stress or various situations in your waking life.
The shadowy figure can also symbolize rejected characteristics of your self. You may be projecting these feelings onto the unknown chaser. Next time you have a chase dream, turn around and confront your pursuer. Ask them why they are chasing you. Perhaps you are running away from something.
-taken from an article on dreammoods.com