Rinse the basil and pat dry. Peel the garlic cloves. In a mortar, mash together 3/4 of the basil leaves and the peeled garlic cloves. Add the pine nuts and grated parmesan, crushing everything together. Stir in 2 tablespoons of olive oil and season with salt and pepper. Preheat the oven to 200°C (392°F) or 180°C (356°F) for convection mode.
Rinse the chicken and pat dry. Cut into 8 pieces. Season all pieces with salt and pepper. Grease a baking dish with the remaining olive oil. Brush each chicken piece with the pesto and place in the dish. Bake on the middle shelf for 40 minutes, turning the pieces several times, until the internal temperature reaches 74°C (165°F).
Bring a pot of water to a boil. Add the tomatoes and boil for about 30 seconds, then transfer to a bowl of ice water to cool. Peel, core, and dice the tomatoes. Top the chicken with the remaining basil and diced tomatoes. Serve.