Cook pasta according to package directions. Meanwhile, rinse chicken; pat dry. Brush chicken, zucchini, and asparagus with 1 tablespoon of the oil; sprinkle all sides with fines herbes and 1/2 teaspoon salt.
Place the chicken in center of the lightly greased rack of an uncovered grill; place the zucchini and asparagus around chicken. Grill directly over medium heat for 12 to 15 minutes or until chicken is tender and no longer pink and vegetables are tender, turning once.
Transfer chicken and vegetables to cutting board; cool slightly. Cut chicken and zucchini into 1-inch cubes; slice asparagus into 1-inch-long pieces. Drain pasta; return to saucepan. Add chicken, vegetables, remaining oil, and thyme to pasta; toss well. Divide among 4 dinner plates; top with cheese and season with pepper. Makes 4 servings.