http://www.how-to-have-a-lucid-dream.com/ Dreams of being chased probably have a deep, evolutionary origin. After all, our ancient ancestors actually were chased by all manner of predators, and this fear of being chased and caught has remained part of our hard wired nature. Even today, after all fears of predation have been removed from our waking lives, dreams of being chased are there to remind us of our earlier animal nature. In modern societies, dreams of being chased can often arise from feelings of general anxiety experienced in the waking hours.