May symbolize running away from or avoiding something because you are afraid of facing or accepting it in waking life.
You may be in denial about some aspect of yourself or something that you said or did.
Being chased by an unknown person or thing may suggest that you are afraid of being caught for something you said or did.
May represent a desire to be pursued or courted by someone.
May be a pun on "being chaste," virginal or innocent.