In a sauté pan, braiser or rondeau, sauté the chicken pieces in abundant olive oil over a moderate flame until golden brown all over.
Add the garlic and season the chicken well with salt and pepper, turning the pieces so they are evenly seasoned.
As soon as you smell the garlic's aroma, drizzle over some white wine and allow it to evaporate, again turning the pieces so they are evenly coated.
Add the tomato and cover. Let it simmer along with the chicken for a few minutes, until it begins to melt into a kind of sauce.
Add the peppers to the pot. Lower the heat, cover and let the chicken and vegetables braise for a good 30-45 minutes, or until the peppers are fully cooked and the chicken is falling off the bone tender.
Uncover the pan and, if there are excess juices, raise the heat and let it cook off a bit, until you have a rich sauce that clings to the chicken.
Serve hot or warm. It is also quite good at room temperature.