If you dream that you are being chased, then such dream indicates the certain situation you are neglecting. Maybe you are afraid of something, therefore you are running from it? If you dream of being chased by some animal, then such dream foretells that you are trying to avoid the animalistic instincts that lie within you. If you were chasing someone in a dream, then such dream foretells that there are certain things you are trying to get as soon as possible. Perhaps you are very impatient person who wants things to happen fast.