Heat a large cast-iron pan or dutch oven to medium-high heat. Dry chicken pieces well with paper towels and season on all sides with salt and pepper.
To the pan, add the olive oil and sear chicken pieces for 3-4 minutes per side. Work in batches and do not crowd the chicken. Place seared chicken pieces on a plate and sprinkle with salt.
When finished with the chicken searing step, turn heat to medium and saute the peppers, onions, and celery until soft (about 7-10 minutes). Add in the garlic and cook for 2 minutes more.
Next, add the white wine and scrape all the flavor bits from the bottom of the pan. Let the wine cook out for 2 minutes then add in the tomato paste, chicken stock, and plum tomatoes.
Stir the sauce together and let it simmer for a couple of minutes. Arrange all the chicken pieces in the pan with the crispiest sides facing upwards. Turn heat to low and simmer covered with the lid slightly cracked open. Cook for 60 minutes or until the chicken is tender.
To finish add the chopped parsley and sprinkle the olives on top. Give it all a stir and serve with crusty bread. Enjoy!