Heat oil in a large skillet over medium heat. Add chicken, onion, and garlic; cook and stir until onion is translucent and chicken is browned, about 15 minutes.

Add squash, chickpeas, undrained tomatoes, broth, carrot, sugar, lemon juice, salt, coriander, and cayenne pepper to the skillet. Bring mixture to a boil, then lower the heat slightly and simmer until vegetables are tender, about 30 minutes.