To dream that you are being stalked indicates some difficulty or issue which you are not confronting. These problems are not going to go away just because you are ignoring them. If you are being stalked in real life, then this fear may be carried over into your dream state.

To dream that you are a stalker represents your shadow and the negative part of your Self. It is also symbolic of a bad habit which you have unsuccessfully tried to break.

*Please See Also Common Dreams: Chase Dreams.