To dream of being chased is commonly in response to something in your waking life that you fear. It is often an emotion of some sort. If this is the case, get up the nerve to turn and face your pursuer. What facial expression do they have? This often reads the feeling that you are trying not to acknowledge. If they look worried, perhaps you have been trying not to fret about something in your life. This dream tells you that you must embrace this concern and deal with it head on. You must worry, and you must accept.
In some rather rare dreams, your assailant can symbolize an actual person in your life. This person has made you feel insecure in one way or another, and until now, you have simply run from them; ignored them; avoided them. This dream is telling you that you can't do this anymore. This person is taking an emotional toll on you, one that you can no longer afford to tolerate. Action must be taken.
Dreams of being chased like this are often recurring nightmares. This means that the sleeping individual wakes up before the awful dream had a chance to end and reveal its secrets. The person goes on to dream it again and again usually, until the subconscious gets its point across. This is because the information is vital to that particular individual's life. Once they become brave and confront their attacker, the dream will generally cease.
If the situation is reversed and it is you who is doing the chasing, this simply means that you are going after your goals. In the dream, ask yourself, 'What am I chasing?' It could be a taxi cab, a bus or anything else for that matter. If you manage to catch it, this foretells luck in your financial and business oriented situation. In most cases however, the dreamer does not catch their target. This simply means that they feel as though they aren't good enough to attain it. They harbor feelings of ill confidence and despair. While they are typically rather intense, such dreams of pursuit are necessary for mental stability. When something is bugging you, your subconscious will tell you, whether you want to hear it or not, so try listening to it keenly always helps.