Heat oven to 375°F. Separate dough into 4 rectangles on ungreased cookie sheet. Press each into 6x4-inch rectangle, firmly pressing perforations to seal.
Spread 1 tablespoon pesto on half of each rectangle to within 1 inch of edge. Sprinkle each with 2 tablespoons cheese; top with chicken and chiles. Fold dough in half over filling; firmly press edges with fork to seal. With fork, prick top of each to allow steam to escape.
Bake 13 to 15 minutes or until deep golden brown. Cool 5 minutes before serving.