Place flour on plate and lightly dredge chicken in flour.
Heat 1 Tbsp. oil in a large pot or Dutch Oven over medium-high heat. Add chicken and cook 3-4 minutes, flip and cook additional 3-4 minutes, or until brown on both sides. Remove from the pan and set aside.
Heat the remaining 1 Tbsp. oil in pot. Add onion and cook 5 minutes, or until softened. Add squash, potatoes and garlic and cook 5 minutes. Stir in broth, oregano, salt and pepper. Add chicken back to pot, tucking it into vegetables. Bring to a boil, reduce the heat to low and simmer, covered, 20 minutes, or until the chicken is cooked through. Sprinkle with additional chopped oregano, if desired.