Combine the carrots and 1 cup water in a saucepan over medium-high heat. Cook until crisp-tender, about 7 minutes; cover and set aside.
Meanwhile, heat a large skillet over medium-high heat. Add the olive oil, then add the chicken and season with salt and pepper. Cook, turning occasionally, until browned and just cooked through, about 4 minutes. Transfer to a plate using a slotted spoon. Add the onion to the skillet and season with 1/4 teaspoon salt. Cover and cook, stirring occasionally, until lightly browned, about 6 minutes. Stir in the cumin and cinnamon; remove from the heat.
Add the couscous, chickpeas, apricots and lemon zest to the skillet. Add the carrots and the hot cooking water (return to a simmer if the liquid has cooled); stir to combine. Add the chicken and any collected juices. Cover and let stand until the liquid is absorbed and the couscous is tender, about 5 minutes; fluff with a fork. Stir in the lemon juice and cilantro. Season with salt.