Whisk together first 6 ingredients.
Place chicken breasts in a heavy-duty zip-top plastic bag; pour half of vinegar mixture over chicken. Place bell pepper, onion, and avocado in a heavy-duty zip-top plastic bag; pour remaining vinegar mixture over vegetables. Seal bags, and chill at least 1 hour, tossing occasionally.
Remove chicken and vegetables from marinades, discarding marinades.
Grill chicken and vegetables, covered with grill lid, over medium-high heat - 350° to 400° F 20 minutes or until chicken is done, turning once. Remove vegetables from grill when done. Cool; cut chicken and vegetables into strips.
Spread tortillas with Avocado Mayonnaise. Place chicken and vegetables on tortillas; roll up. Cut in half diagonally.
Peel avocados, and mash in a small bowl; stir in mayonnaise and remaining ingredients. Cover and chill.Makes about 1 1/2 cups