Heat the oil in a deep nonstick saucepan, add the onion and cook for 3 minutes until soft. Add the curry paste and cook, stirring, for 1 minute.
Add the chicken, tomatoes, broccoli and coconut milk to the pan. Bring to the boil, then reduce the heat, cover and cook over a low heat for 15–20 minutes.
Remove from the heat, season well with salt and pepper and serve immediately.