Dreams of being chased often signal avoidance of challenging situations, stemming from feelings of insecurity. When animals chase you, it reflects hidden anger projected onto them, or a flight from primal instincts. Chasing someone in a dream symbolizes your pursuit of difficult goals or possibly repressed aggression. If you're chased and enjoy it, it indicates a desire to be wanted and may parallel a budding relationship.
**For an in depth analysis, You Can Also Read Common Dreams: Chase Dreams.