Put the cream cheese, chives and garlic in a food processor and blitz until you have a smooth green purée. Line a small shallow bowl with cling film and transfer the cream cheese to the bowl. Cover and freeze for a couple of hours until solid.
Preheat the oven to 200°C/fan 180°C/gas mark 6. Cut a large incision in each chicken breast to create a pocket. Remove the cream cheese from the freezer and cut into 4 pieces. Stuff each chicken breast with a piece, making sure the chicken breast completely covers the filling.
Put the flour, egg and breadcrumbs into three separate bowls. Dip the chicken breast in flour first, then the egg and then the breadcrumbs. Transfer to a baking tray. Spritz each chicken breast evenly with the olive oil spray, then bake in the oven for 30-35 minutes until golden and the chicken is cooked through. Serve with a side salad.