In the container of a food processor or blender, place 1 tb of the olive oil, 1 tb of the vinegar, 1/4 tea each mustard, salt and pepper; process 15 seconds. While processor is running, add 2 more tb olive oil and process 10 seconds. Add remaining 3 tb vinegar, remaining 3 tb olive oil, garlic, and lemon peel. Finally add chives and process about 15 seconds more.

Dip each piece of chicken in sauce and coat well. Marinate in refrigerator at least 4 hours (or overnight).

Place chicken on prepared grill, skin side up, about 8 inches from heat. Sprinkle with remaining 3/4 ts salt and 1/4 ts pepper. Grill, turning and basting with sauce every 10 minutes, about 1 hour or until fork can be inserted into chicken with ease.