Puree the basil, pine nuts, cheese and olive oil in a food processor.
Season to taste with salt.
The Chicken
Preheat oven to 375°F.
Lay 2 slices of the prosciutto flat onto a work surface, overlapping them slightly along their long edge, to form a large rectangle.
Place a chicken breast lengthwise at the short end and slit it open along one side to create a wide pocket. Spoon in some of the pesto and then wrap the prosciutto neatly around it. Repeat for the other 3 breasts.
Place on a baking sheet, seam side down and bake until golden and cooked through, about 15 minutes.
Lay 2 slices of the prosciutto flat onto a work surface, overlapping them slightly along their long edge, to form a large rectangle.
Place a chicken breast lengthwise at the short end and slit it open along one side to create a wide pocket.
Spoon in some of the pesto and then wrap the prosciutto neatly around it.