Add olive oil and onion to a cold skillet. Place over medium heat, season with a pinch of salt and cook, stirring often, until golden brown, around 18 minutes. Remove from heat and set aside to let cool.
In a large bowl, combine the ground chicken, garlic, sun-dried tomatoes, oregano, dried basil, sautéed onions, salt and pepper. Mix well with your hands until combined. Divide the mixture into 6 equal parts (or 8 parts for smaller, 1/4 lbs burgers). Form into patties using the ‘baseball and glove technique outlined above’ and brush both sides with avocado oil.
Preheat your grill to medium-high heat. If using a Traeger, preheat to 500F. Place the burgers over direct heat (or towards the back perimeter on a Traeger) and grill until grill marks form, around 6 minutes. Flip and continue cooking until the thickest part of the burgers reach 165F internally, around 4 more minutes.
Transfer the burgers to a serving platter and serve with lettuce buns, onions, tomatoes, pickles and Basil Aioli.