Place chicken in a large saucepan and add enough water to cover. Bring to a simmer over medium heat. Reduce heat to maintain a simmer, cover and cook until the chicken registers 165°F with an instant-read thermometer, 12 to 15 minutes. Transfer to a cutting board. Let stand until cool enough to handle, then chop or shred. Refrigerate until cold, about 30 minutes.
Combine yogurt, mayonnaise, tarragon, salt and pepper in a large bowl. Add the cold chicken, celery, grapes (if using) and pecans; stir to combine.
To serve, fill each avocado half with about ½ cup chicken salad. (Refrigerate the extra chicken salad for up to 3 days.)