Dream about chased by someone is a metaphor for an escape from your own personal issues and stresses. You are trying to appear innocent to others. You need to be careful in who you trust and who you confide in. This is an evidence for aspects of yourself which you have kept hidden inside. You are trying to take the quick and easy path to success.
Chased by someone dream means control over your emotional desires. You are building up a layer of protection. You are giving more than you are getting back. The dream signifies your generosity and giving nature. Perhaps you are being too frigid.
If you dreamt about chased by someone:
A key word for you is compromise. You have been very stubborn with regard to a certain issue for the past few days. Now you need to give, in order to receive. Meet people halfway instead of insisting that things only be done your way.