In a large pot, heat the olive oil over medium heat. Add the chicken pieces and cook until browned on all sides, about 5-7 minutes. Remove the chicken and set aside.
In the same pot, add the diced onion and cook until translucent, about 3-4 minutes. Stir in the minced garlic and cook for an additional 1 minute.
Add the carrots, potatoes, and green beans to the pot. Stir to combine.
Return the browned chicken to the pot. Pour in the chicken broth and add the thyme, rosemary, salt, and pepper. Bring to a boil, then reduce the heat to low and let simmer for 30-35 minutes, or until the vegetables are tender.
If you prefer a thicker stew, mix the flour with a few tablespoons of water to create a slurry. Stir this into the stew and cook for an additional 5 minutes until thickened.
Taste and adjust seasoning if necessary. Serve hot, garnished with fresh parsley.