If you are being chased in a dream then you are running from some issue or confrontation in waking life. What or whom are you avoiding? Is it something from your past you don’t want to deal with? Is it a secret you don’t want exposed? Is it a commitment you are trying to get out of? Or is it a confrontation you know you need to have but hope it will go away if you ignore it long enough?
The message of this dream is that you cannot run from this issue forever. The longer you ignore or avoid it, the more it will follow you.
If you are chasing something or someone in your dream then you may be up against a deadline in waking life, perhaps even a self-imposed deadline. Or there is a goal you have for yourself and you feel you are running out of time. Get on the ball!