Chicken Cacciatore means hunter style, the french version is called Poulet Chasseur. The dish should include mushrooms, meat broth or sauce and tomato (sauce). This is a favorite of my family and here is my fairly easy version. I always use dark meat because this is a braised dish and I like what braising does with dark meat, where breast meat will often dry out. If you do use the breast you may want to pull it out early in the cooking process and add it later to finish.
In a dutch oven or large pot add about 2 Tablespoons olive oil and heat pan on high. When hot add seasoned chicken, I used boneless skinless thighs tonight, but you can use bone in just as easily. Brown the chicken pieces well. Add 1 chopped onion, 2 chopped carrots, 1 stalk chopped celery and 3 cloves chopped garlic and about 8-10 sliced mushrooms. Saute a bit and if you like add about 1/2 cup red wine and reduce. I also added dry porcini mushrooms because I had them and they add good flavor. To use dried mushrooms, place a handful in a glass bowl and pour boiling water to just cover. When reconstituted gingerly remove mushrooms and strain liquid into the cooking pot. Add soaked mushrooms to pot.
Add about a cup of chicken broth and a can whole peeled tomatoes, crushed and a sprig of rosemary and a few grinds of black pepper. See my note on canned tomatoes here. Bring to a boil, reduce to low and simmer covered till meat is very tender. Remove meat from pot and reduce sauce to a thicker consistency if necessary. Check seasoning. Serve with creamy polenta.