Place the cooked shredded chicken in a large bowl and add the thinly sliced green onions.
In a small bowl, whisk together the Greek yogurt, mayonnaise, diced chipotle pepper, adobo sauce, lime juice, lime zest, and a big pinch of kosher salt and black pepper until smooth.
Pour the dressing over the chicken and green onions and toss until the chicken is evenly coated; taste and adjust salt and pepper as needed.
Just before serving, gently stir in the chopped avocado so it stays fresh and slightly chunky.
Serve the salad on toast, crackers, chips, in lettuce cups, or over greens, and top with pickled onions if desired.
Store leftovers in the refrigerator for a few days; stir before serving.