Spray a 9" x 12" (or 8.5" X 12.5") baking dish with non-stick spray, then spread 1/4 cup basil pesto over the bottom of the dish.
Lay chicken strips over the pesto, then spread 1/4 cup more basil pesto over the chicken.
Cover the baking dish with aluminum foil (or use a baking dish with a tight-fitting lid) and bake the chicken for 25-30 minutes, just until chicken is barely firm and cooked through. (Don't cook too much at this point, or the chicken will be overcooked by the time the cheese is melted and browned.)
Remove foil and sprinkle chicken with 1/2 cup grated mozzarella cheese. Put dish back into the oven without foil and cook 5 minutes more, just until cheese is melted. (If your broiler is separate from the oven, start preheating it when you take the chicken out.) Melt cheese for 5 minutes and switch oven to broil and broil for 5 minutes more, just long enough to get the cheese lightly browned.
Serve hot. There will be some flavorful juice in the bottom of the dish when this is done, so you may want to serve with rice, couscous, or quinoa to soak up the juice, but if you're eating this for your diet, just spoon the juice over the chicken.