Pat the chicken dry with a paper towel, then season generously on all sides with kosher salt and black pepper.
Heat olive oil in a large pan over medium-high heat. When hot, add chicken thighs skin-side down, working in batches as needed, and cook until browned on both sides. Transfer to a large plate, then reduce the heat to medium.
Add sliced onion, then season with kosher salt. Cook, stirring occasionally, until softened. Add chopped garlic, paprika, ground cumin, ginger, turmeric, ground cinnamon, and cayenne pepper. Cook, stirring occasionally.
Pour in low-sodium chicken broth, then use a spatula to scrape up any browned bits from the bottom of the pan. Stir in halved green olives and the chopped preserved lemon. Return the chicken to the pan. Lower the heat to a simmer, then cover the pan and cook.
Taste the sauce, adjust the seasoning as needed, then transfer the chicken pieces to a large platter. Spoon the sauce on top, then sprinkle with chopped fresh cilantro and additional lemon rounds or wedges for serving. Enjoy immediately with couscous!