Tear lettuce into pieces and place in large bowl.
Set aside.
Add onion, pepperoncini, tomato, cucumber, black olives and avocado.
Combine 2 tablespoon of olive oil, lemon juice, Italian seasoning, 1 teaspoon of salt, pepper, and vinegar into a jar and chill.
Meanwhile, preheat the grill on high for 15 minutes.
Place the chicken breasts in a pan and pour the lime juice over them.
Add salt, and 1 tablespoon of olive oil.
Coat well.
Place the chicken breasts on the grill, reduce heat to medium and cook for 10 minutes, then flip and cook for 5 minutes more.
Remove from heat, slice into strips and place on top of the salad.
Pour chilled dressing over top and toss well.
Serve.