Brown the Chicken: Season the chicken with salt and pepper. Heat oil in your large pot. Place chicken skin-side down in the hot oil.
Cook until the skin is very crispy and brown. Remove the chicken and set it on a plate.
Sauté the Vegetables: Add onions and peppers to the same pot. Cook them until they start to get soft.
Throw in the mushrooms and cook more. Add the garlic at the very end. Do not let the garlic burn or turn bitter.
Deglaze the Pan: Pour the red wine into the hot pan. Use your spoon to scrape the bottom. Those brown bits have all the best flavor.
Let the wine bubble and reduce by half. This removes the harsh alcohol taste.
Simmer the Sauce: Stir in the tomatoes and chicken stock. Add the rosemary and the salty capers.
Put the chicken back into the red liquid. Cover the pot with a tight lid. Let it simmer on low for thirty minutes.
Finish and Serve: Take the lid off for the last minutes. This helps the sauce get nice and thick. Check if the chicken is fully cooked through.
Taste the sauce and add more salt if needed. Serve it hot with your favorite side dish.