Process anchovy fillets and 3/4 cup green olives in a food processor until chopped, stopping to scrape down sides; set aside.
Sprinkle chicken with salt and pepper. Brown chicken on all sides in hot oil in large skillet over medium-high heat. Remove chicken, reserving 2 teaspoons drippings in skillet; add garlic, and sauté 1 minute. Add white wine and vinegar; cook 2 minutes stirring to loosen browned particles. Stir in anchovy mixture and 2 tablespoons water.
Return chicken to skillet, turning to coat pieces in sauce.
Cook, covered, over medium-low heat 45 minutes or until chicken is tender. (Stir in additional water, if needed.)
Add 3 tablespoons lemon juice, Italian parsley, and remaining 3/4 cup green olives; cook 1 to 2 more minutes. Serve immediately.