Preheat oven to 225°C/ gas mark 7. Line 2 baking trays with baking paper and set aside.
Mix flour and water in a bowl until it forms a sticky dough. Turn out onto a floured bench and knead the dough for about 8 minute until it becomes silky.
Divide it into 6 portions. Shape each portion into a 15cm flat round and pour a tablespoon of pesto over each one.
Divide the chicken and cheese equally among the 6 rounds. Make sure to only put them on one side.
Lightly brush a little water on the edges and pull over one side to create a turnover. Press edges together with a fork. Place on tray. Brush a little water over the tops of the turnovers.
Bake for 25-30 minutes.