It is obviously a very important dream, especially since you have such a good recollection of it.
I think that dreams need to be analyzed together with going ons in persons life. In that respect, there is very little that can be connected between the dream and reality, as we don't know your reality. But, your lack of self confidence, stuttering, and the dream itself point, in my view, to an abusive family or at least one of the parents or guardians or relatives who was physicaly close to you.
Some possibly good questions: were you ever chased around the house by someone who was close to you? Like father or mother chasing you to beat you up for messing up (in their view) something? Or maybe the chase had a "fun" tone to it, with you being some sort of a victim of someone's rough and/or sick sense of humor?
Can you remember the house that the chase happened in? Do you have a feeling of whether it was your house, or someone elses? (It most likely felt like your house, even if it didn't look like the one you lived in).
Don't know if you read it - "Toxic Parents" seems to be a very good book. I only read a few bits and pieces, but from observing experiences of someone very close to me, I can tell you that the whole problem of stuttering and low self esteem comes from parents or parent figures in your childhood. The moment you distance yourself from them, and realize you owe them no explanations or even any contact, will be the moment your new life starts. Not before then.
The responsibility in a parent/child relationship is a one way street: your parents have a God given responsibility to take care of you, with love, support, so that you can become independent, and in turn you owe the same to your kids. Whether you'll stay in touch with them, is strictly a matter of personal preference, just like you are not obliged to be freinds with every person you run into. If your parents do not appreciate you as a person, which bad parents usually show through physical abuse, put downs, cynicism, criticism, they are a poison in your life, and are best avoided forever.
They say "it is never too late for a happy childhood".