Dreams about being chased often stem from feelings of anxiety in your waking life.
The way we as humans respond to anxiety and pressure in real life is typically manifested as a chase dream.
Running is an instinctive response to physical threats in our environment. Often in dream scenarios, you are being pursued by an attacker (can be human, could be an animal) that wants to hurt, or possibly kill you.
Dreams about being chased may represent your way of coping with fears, stress or various situations in your waking life. Instead of confronting your problems, you are running away from them and avoiding them.
The pursuer or attacker who is chasing you in your dream may also represent a part of yourself.
Your own feelings of anger, jealousy, fear, and possibly love, can assume the appearance of threatening figure. 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.
A more direct analysis of chase dreams is the fear of being attacked.
Such dreams are more common among women than men, who may feel physically vulnerable in the urban environment. These dreams are inspired by fears of violence and sexual assault in which we are so over-exposed from the media.
The violence that the media portrays magnifies our fears and how at risk we all are.