Bring the vinegar and sugar to the boil in a small saucepan, then reduce the heat to low and simmer for 15 minutes until slightly thickened. Remove from the heat and set aside to cool.
Pat the chicken dry and season well. In a medium frying pan with a lid, add the oil over a medium/high heat until hot. Add the chicken to the pan and cook for 3 minutes on each side until golden brown and almost cooked through.
Top each piece of chicken with a slice of mozzarella, cover with a lid and cook for a further 4 minutes until the mozzarella has melted and the chicken is completely cooked through.
Remove the pan from the heat and scatter over the tomatoes. Scatter over the basil and olives and drizzle with the balsamic glaze. Serve with lots of crusty bread to mop up the juices from the pan.