Being chased is a classic anxiety dream. Tradition reads the pursuer as something you are avoiding — a task, a feeling or a decision — that keeps catching up. Being chased by an unknown figure points to an anxiety without a clear name. A chaser you recognise is linked to tension with that person or with the trait they represent. Being caught is read as finally facing the issue, often less frightening than expected; escaping successfully stands for postponing rather than resolving. Turning around to face the pursuer is read as courage; it can help to ask what you are running from in waking life.
Does the traditional reading fit your dream, or did it mean something else to you?
My Cosmic Code has a private dream journal. Write a dream down and the app picks out the symbols in it, shows what dream books say about them and, over time, which words recur across your entries. The journal is stored on your device only.