1. Heat the oil in a large non-stick frying pan. Add the prosciutto and fry for about 2 minutes until crisp. Remove with a slotted spoon, letting any fat drain back into the pan, and set aside. Put the onion and garlic in the pan and fry for 3-4 minutes.
2. Spread the onion out in the pan, then lay the chicken breasts on top. Season with pepper and fry for 5 minutes over a medium heat, turning the chicken once, until starting to brown on both sides and the onion is caramelising on the bottom of the pan. Remove the chicken and set aside on a plate. Turn up the heat to high, give it a quick stir and, when it is sizzling, pour in the wine and let it bubble for 2 minutes to reduce slightly.
3. Lower the heat to medium, return the prosciutto to the pan, then stir in the tomatoes (breaking them up with your spoon), tomato purée and mushrooms. Spoon 4 tbsp of water into the empty tomato can, swirl it around, then pour it into the pan. Cover and simmer for 15-20 minutes or until the sauce has thickened and reduced slightly, then return the chicken to the pan and cook, uncovered, for about 15 minutes or until the chicken is cooked through. Season and scatter over the basil and olives to serve.