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 degrees for 20 minutes or until chicken is done, turning once.
Remove vegetables from grill when done.
Cool; cut chicken and vegetables into strips.
For mayo: Peel avocados, and mash in a small bowl; stir in mayonnaise and remaining ingredients.
Cover and chill.
Spread tortillas with Avocado Mayonnaise.
Place chicken and vegetables on tortillas; roll up.
Cut in half diagonally.