Heat 1 tablespoon of the olive oil over medium heat in a large sauté pan (big enough to hold all the chicken pieces) or Dutch oven.
When hot, add the onions and cook for about 8 minutes until softened and lightly browned. Add the garlic, lemon zest, ras al hanout, and 3 tablespoons parsley (save the rest for garnishing). Cook, stirring, 1 minute more. Transfer the mixture to a medium bowl.
Season the chicken breasts with salt and pepper.
Heat the remaining 1 tablespoon of olive oil over medium-high heat and, working in batches if needed, cook the chicken until lightly browned on both sides. Transfer to a plate or rimmed baking sheet.
Add the chicken broth to the pan, increase the heat, and scrape with a wooden spoon to loosen all of the browned bits.
Return the chicken and onion mixture to pan. Bring to a boil, then cover and reduce the heat. Simmer for about 15 minutes.
Add the artichokes, fennel, and carrots to the pan. Cook, covered, for about 15 minutes. Add the olives and continue cooking for another 10 minutes or so. The vegetables will be crisp-tender.
Serve garnished with the remaining parsley.
*Ras al hanout is a North African spice mixture that may be purchased in some specialty stores or you can make your own by combining the following: