Being chased by a dragon is the chase dream at maximum scale — in the East great fortune or great authority pressing toward you (the tradition suspects you're fleeing something that wants to crown you), in the West the Self's biggest energy demanding relationship, in Ibn Sirin's frame a mighty matter or adversary in pursuit.
Three readings
In Western psychology · Jungian
When the Shadow grows this large, Jung would say the avoided material is no longer a quirk but a life-force: the dragon chasing you is your own biggest energy — ambition, rage, calling, sexuality — grown enormous on neglect. It pursues because scale demands relationship; you cannot pocket a dragon. The classic move applies at maximum stakes: stop, turn, and ask what it guards — dragon-chases in dreamwork famously convert to dragon-riding once faced.
The Eastern reading carries a sly reversal: the dragon is fortune and authority, so a dragon in pursuit may be greatness pressing toward the dreamer who keeps declining it — promotion, responsibility, a destiny-sized task. Flight from the dragon reads toward avoidance of the large life asking for you. Where the dream feels purely fearsome, the older entries allow the other face: mighty authority — an institution, a patriarch, the state — bearing down. Which it is, your waking life already knows.
Reasoned from serpent and pursuit together, the corpus reads a great serpent in chase toward a formidable matter or adversary actively pressing — a dispute of size, an authority's attention, a temptation with real teeth. The scale counsels seriousness, not despair: what pursues in dreams is met, in the tradition, by fortifying oneself — prayer, rectitude, and settling the matter's worldly causes. As meaning: something too large to outrun asks to be faced with your affairs in order.
Is a chasing dragon good or bad in Chinese tradition?
Double-faced, deliberately: the dragon is fortune and authority, so pursuit reads either as greatness seeking you or as great power pressing you. The honest test is waking life — is something large currently asking for you (a role, a duty), or bearing down on you (an authority, a debt)?
The dragon breathed fire at me — what does that add?
Fire adds urgency and temper: the great force is no longer patient. In the West, suppressed material erupting; in the East, authority's displeasure or fortune demanding immediate answer. It usually marks the season where avoiding has started to cost.
I turned and the dragon stopped — did I win?
That's the dream's best ending: pursuit converts to audience. Across traditions, the great force facing you quietly is power waiting to be engaged — the classic follow-up is that later dreams feature the dragon as ally or mount.
This is the general reading. Your dream is specific.