How to Make It
Make the chicken In a large bowl, whisk the olive oil with the lemon juice, garlic, salt and spices. Add the chicken and onions and turn to coat in the marinade. Cover and refrigerate for 1 hour or overnight.
Preheat the oven to 450°. Line a large rimmed baking sheet with foil and arrange the chicken on it skin side up. Add the onions. Scrape any remaining marinade in the bowl over the chicken. Roast for about 40 minutes, until the chicken and onions are browned and the chicken is cooked through. Transfer the chicken to a cutting board and coarsely shred with a knife and fork.
Meanwhile, make the salad In a small bowl, whisk the crème fraîche with the lemon zest and 1 teaspoon of the lemon juice; season with salt. In a medium bowl, whisk the remaining 2 tablespoons of lemon juice with the olive oil; season with salt and pepper. Add the lettuce, cilantro, scallions and jalapeño and toss to coat. On a large platter, arrange the salad with the chicken, onions, pita bread and olives. Serve with the lemon crème fraîche alongside.