To prepare chicken breasts without using any fat, choose poaching. Heat them in barely simmering water for a few minutes, then let stand in the liquid until cooked through. They will stay moist and tender -- perfect for cold salads.
Place chicken in a large straight-sided skillet or pot. Add water to cover and season with salt. Bring to a boil, cover, and reduce to a bare simmer; cook 5 minutes. Remove skillet from heat and let chicken stand, covered, until cooked through, 12 to 14 minutes. Remove chicken from liquid and let cool completely.
Shred chicken with two forks. In a large bowl, whisk together vinegar and oil and season with salt and pepper. Add chicken, celery, and tarragon; toss to combine. Serve over lettuce leaves.