Heat 2 tablespoons of the oil in a large frying pan, add the chicken breasts and cook over a medium heat for 5 minutes, turning frequently, until browned all over. Remove from the pan with a slotted spoon and drain on kitchen paper.
Heat the remaining oil in the pan, add the onion slices and pesto and cook, stirring constantly, for 3 minutes until the onion is softened but not browned.
Add the wine and measurement water to the pan and bring to the boil. Return the chicken breasts to the pan and season with salt and pepper to taste. Reduce the heat and simmer for 15 minutes, or until the chicken is cooked through.
Stir in the grapes and serve immediately, garnished with basil leaves.