Heat oven to 200C/180C fan/gas 6. Mix the peppers and onion on a big baking tray with half the oil. Transfer to the oven and cook on the top shelf for 10 mins.
Meanwhile, carefully make a pocket between the skin and the flesh of each chicken breast, but don’t pull off the skin completely. Push equal amounts of cheese under the skin, smooth the skin back down, brush it with the rest of the oil, season, then add to the tray along with the tomatoes and olives. Return to the oven and cook for 25-30 mins more until the chicken is golden and cooked. Serve with baked potatoes, if you like.