For The Pesto, grate the cheese. Mash the garlic with the salt to form a smooth paste. Combine the garlic paste, basil, pine nuts, and olive oil in food processor or blender. Puree until smooth. Stir in the cheese. NOTE: Can be made to this point several hours ahead. COOKING AND SERVING: Heat the grill or broiler. Toss the chicken with vegetable oil and sprinkle with salt and pepper. Broil or grill the chicken, turning once, until just cooked through, about 10 minutes total. Cut into bite-size pieces. Cook pasta in boiling, salted water until tender, about 3 minutes for fresh pasta. Drain and return to pot. Toss with chicken and pesto sauce and season with salt and pepper. Serve warm or at room temperature. Makes 4 servings. [COOKS March-April 1988]