Preheat oven to 170C/150C fan forced. Heat half the oil in a large flameproof casserole dish over high heat. Add the chicken and cook, turning, for 2-3 minutes or until browned. Transfer to a plate.
Add the remaining oil to the dish and heat over medium heat. Add the carrot and onion. Cook, stirring, for 6-7 minutes or until the mixture softens. Add the garlic and curry paste. Cook, stirring, for 1-2 minutes or until aromatic. Add the cinnamon, tomatoes and 300ml water. Stir until combined then bring to the boil.
Return the chicken to the dish and cover. Bake for 1 hour 20 minutes. Add the chickpeas and beans. Stir until combined. Cover and bake for a further 20 minutes or until the chicken is cooked through. Remove and discard the cinnamon.
Add the spinach and stir until wilted. Top the curry with the yoghurt. Serve with lime wedges.