Preheat the oven to 200C/ Gas 6/fan oven 180C. Spread the potatoes, zucchini, pepper and tomatoes in a shallow roasting tin and scatter over the olives. Season with salt and coarsely ground black pepper.
Slash the flesh of each chicken breast 3-4 times using a sharp knife, then lay the chicken on top of the vegetables.
Mix the olive oil and pesto together until well blended and spoon evenly over the chicken. Cover the tin with foil and cook for 30 minutes.
Remove the foil from the tin. Return to the oven and cook for a further 10 minutes until the vegetables are juicy and look tempting to eat and the chicken is cooked through (the juices should run clear when pierced with a skewer).