81.5 %said they'd been chased: the top dream of 55
Being chased is one of the most commonly reported dreams. In a survey of 1,181 Canadian university students, 81.5 % said they had ever dreamed of being chased or pursued without being hurt: the most common of 55 typical dreams in that study, and also the dream most often named as the first one people remember.
In the Typical Dreams Questionnaire study (Nielsen et al., 2003), "being chased or pursued, but not physically injured" was the most prevalent theme: 81.5 % overall, 83.1 % of women and 77.7 % of men. (For men alone, sexual dreams ranked first.)
It topped the list in that survey of young, mostly female Canadian students; other samples rank themes differently, so it isn't "the most common dream in the world". The figure counts people who have ever had the dream, not how often it happens.
Often the first dream we remember
Asked which typical dream they remembered having first, more students chose being chased (21.6 %) than any other theme.
What a chase dream does not mean
Dream dictionaries give the chase a fixed meaning. Research doesn't support one meaning per dream: what the studies show is how common a dream is and what it goes with in the people studied.
Questions
Is it normal to dream about being chased?
Yes. In a large student survey, about four in five people said they had ever had a chase dream.
What does it mean when you dream someone is chasing you?
Research doesn't give it a fixed meaning. What studies show is that it's one of the most common dreams of all, and often the first one people remember.
Sources
Nielsen, T. A., Zadra, A. L., Simard, V., Saucier, S., Stenstrom, P., Smith, C., & Kuiken, D. (2003). The typical dreams of Canadian university students. Dreaming, 13(4), 211–235. https://doi.org/10.1023/B:DREM.0000003144.40929.0b
73.8 %of students said they'd dreamed of falling
18.8 %said they'd dreamed of losing their teeth
67.1 %said they'd dreamed of school or studying