HALVE PEPPERS, removing stems, seeds, and large ribs. Set aside half of each color. Dice remaining pepper halves and place in a nonreactive bowl with the remaining salsa ingredients. Stir well. Allow salsa to meld at room temperature for at least 1 hour before serving. Taste and adjust seasonings as desired.
Cut remaining pepper halves into strips and small star shapes for garnish; dice trimmings and add to salsa.
PLACE CHICKEN breasts in a big resealable plastic bag. Whisk remaining ingredients together to make a marinade and pour over chicken. Seal bag and place in refrigerator for several hours or overnight, turning occasionally.
Heat barbecue cooker to glowing. Remove chicken from marinade; pour marinade into a small bowl. Spray grill with nonstick vegetable spray and place 4 to 6 inches from medium-hot coals. Put chicken on grill and cook, basting with marinade and turning occasionally, until chicken is cooked through. Allow about 6 to 8 minutes per side, until juices are no longer pink.
Place dollops of salsa on each serving plate and put a chicken breast half in the center. Garnish with the pepper stars.