Season the chicken all over with salt and pepper. Heat the olive oil in a large skillet over medium-high heat. Add the chicken and cook until browned, 4 to 5 minutes per side. Remove to a plate.
Add the squash and onion to the skillet and cook, stirring occasionally, until softened and lightly browned in spots, about 3 minutes. Add the garlic and cook until softened, about 30 seconds. Add the turmeric, cinnamon stick and raisins and stir to coat the vegetables.
Add the lemon zest and chicken broth to the skillet and bring to a simmer. Return the chicken to the skillet and reduce the heat to maintain a steady simmer; cover and cook until the chicken is cooked through, 10 to 12 minutes.
Transfer the chicken to plates. Stir the lemon juice into the broth and season with salt and pepper. Spoon the broth and vegetables over the chicken and top with cilantro.