Heat olive oil in a large Dutch oven or heavy pot over medium-high heat. Season chicken pieces with salt and pepper, then brown in batches. Remove and set aside.
In the same pot, add onion and cook until softened, about 5 minutes. Add garlic and cook for 1 minute until fragrant.
Add carrots, celery, and potatoes. Stir to combine and cook for 5 minutes.
Pour in white wine (if using) and scrape up any browned bits from the bottom of the pot. Let simmer for 2–3 minutes.
Return chicken to the pot. Add chicken broth, bay leaves, thyme, and rosemary. Bring to a boil, then reduce heat to low, cover, and simmer for 1 hour.
Stir in frozen peas and continue to simmer, uncovered, for 15–20 minutes, or until vegetables are tender and stew has thickened slightly.
If a thicker stew is desired, mix 2 tablespoons of flour with 1/4 cup water to make a slurry. Stir into the stew and cook for 5–10 minutes until thickened.
Remove bay leaves. Taste and adjust seasoning with salt and pepper. Garnish with fresh parsley before serving.
Notes
Serve this comforting chicken stew with crusty bread or over mashed potatoes for a complete meal. Leftovers taste even better the next day as the flavors continue to meld.