Preheat the oven to 220C/425F/Gas 7. Halve or quarter the potatoes, depending on their size (to produce evenly sized chunks). Place in a large non-stick roasting tin. Toss with two tablespoons of the oil and season to taste with salt and pepper, then put into the oven for 15 minutes.
Cut the chicken thighs in half, add the smoked paprika and cinnamon, if using. Scatter with half the thyme leaves, season with salt and pepper, stir through and set aside.
Make a nick in the skin of the chorizo then, peel away the papery skin. Cut the sausage into chunks or rounds.
When the potatoes have had 15 minutes roasting, give them a stir, then nestle the chicken and tomatoes into the pan. Scatter with the chorizo, garlic and the remaining thyme leaves, then season with salt and pepper.
Drizzle the remaining oil all over, and return to the oven to roast for 20 minutes more, stirring half-way, until the chicken is cooked through and the potatoes and tomatoes are turning golden brown and crisp at the edges
Scatter the dish with a handful roughly chopped parsley, and serve.