This kind of dream is common among children. Often, it reflects a deeply held fear of the animal doing the chasing. However, it may reveal an anxiety about something completely separated from the animal kingdom. In cases like this, it is important to think about what is chasing you and what your experiences have been with that particular animal.
For example, if a relative whom you did not particularly like had a German shepherd dog, you may dream about being chased by the dog. This may reveal either the desire of the relative to obtain your attention and affection, or it may validate your fears and anxieties about that person.
If you often use animal characterizations of people's personalities, this may be particularly telling. (He's a bear, she's a momma bear, he works like a horse, etc.)
Depending on who the others are, it may be useful to determine what common relationship exists among your persecutors. You may feel indebted to them or simply hated by them. The former may include people with whom you feel an emotional or financial indebtedness. The latter is a throwback to the old schoolyard scuffle. You may feel that particular co-workers are angry or jealous and are seeking your life or expulsion. If you are chased by strangers, this may have more global implications for how you see yourself in the world.
During different seasons in life, many people experience a sense of not fitting in, or of being driven away. This feeling may come immediately prior to or immediately following a geographic move into a new region of the country. It may also occur around other times of transition such as marriage or a career change. This type of dream usually reflects acceptance anxiety. In dreams where you are being chased, the emotion of the dream is often as important as the objects and images of the dream.
Did you feel your life was threatened?
Did you feel that you could have turned and faced the chaser with relative success? These questions will help determine the interpretation of such dreams.