In a shallow bowl, combine the chicken breasts, 2 tablespoons of the olive oil, juice of half a lemon, garlic, marjoram, thyme, oregano, salt and pepper. Toss to coat, cover and refrigerate 1 to 4 hours.
When ready to cook, preheat your Traeger Grill to 500 F.
Drizzle both sides of the red onion slices with a small amount of olive oil and lightly season with salt and pepper.
Place the chicken breasts and red onion on the grill, close the grill door and cook until grill marks form, around 6 minutes. If using a conventional grill, cook the chicken over medium heat. Flip and cook the other side until grill marks form and the thickest part of the chicken registers 160F. Transfer the chicken and onions to a board and cover with foil to keep warm. Let the chicken rest at least 5 minutes before slicing.
In a large bowl, combine the lettuce, green onion, cucumber, tomatoes, and dill. Drizzle with 2 tablespoons olive oil and the remaining lemon juice. Lightly season with salt and pepper to taste and toss to coat.
To serve, spoon the whipped feta onto individual plates. Top with the salad and sliced chicken. Garnish with pickled pepperoncini peppers and enjoy immediately.