In a small bowl, whisk together the vinegar, orange juice, oil, ½ teaspoon salt, and ⅛ teaspoon pepper until well blended.
Cook the chicken breasts in boiling, salted water for 10 minutes or until the chicken is no longer pink inside.
Remove the chicken and cool 5 minutes on a cutting board before slicing into long strips.
Transfer the warm sliced chicken to a bowl and toss with a few tablespoons of vinaigrette. Season to taste with salt and pepper.
With a sharp knife, remove the orange peel and white pith from the oranges. Slice crosswise into thin rounds.
In a large bowl, toss the onion and lettuce with the remaining vinaigrette. Divide between bowls and top the salads with the chicken, oranges, and avocado slices.