Preheat a grill or stovetop grill pan over high heat.
Rinse and dry chicken, then drizzle with olive oil and season with salt and pepper.
When grill or pan is very hot (almost smoking), place chicken on grill.
Cook until internal temperature is 165°, 5 per side.
Set aside to rest for 2 to 3, then shred using 2 forks.
Meanwhile, prepare dressing.
In a medium jar add mayonnaise, olive oil, red wine vinegar, garlic, red onion, chives, salt and pepper; shake well.
Keep in fridge until ready to serve.
Serve each iceberg wedge with half an avocado, a handful of shredded chicken and a drizzle of salad dressing.
Garnish with chives.