Preheat the oven to 350°F (175°C). Prepare a 9×13-inch baking dish and set it aside.
Pour half of the reserved artichoke marinade into a large skillet over medium-high heat. Add the chicken pieces and cook for 8–10 minutes, stirring occasionally, until the chicken is browned and most of the liquid has evaporated.
Using a slotted spoon, transfer the browned chicken pieces to the baking dish, spreading them evenly across the bottom.
Pour the remaining artichoke marinade into the same skillet. Add the sliced onion, minced garlic, mushrooms, oregano, basil, salt, rosemary, and black pepper. Cook for 5–8 minutes, stirring frequently, until the onions become translucent and the mushrooms begin to soften.
Add the diced tomatoes with their juice, tomato sauce, sliced black olives, and chopped artichoke hearts. Stir thoroughly to combine the vegetables, herbs, and tomato sauce.
Pour the prepared sauce evenly over the chicken in the baking dish. Cover the dish securely with aluminum foil.
Bake in the preheated oven for approximately 45 minutes, or until the sauce is bubbling and the chicken is cooked through. The chicken should reach an internal temperature of 165°F (74°C).
Carefully remove the foil and drizzle the Madeira wine evenly over the chicken and sauce. Sprinkle the shredded mozzarella cheese across the top.
Return the uncovered baking dish to the oven and bake for approximately 10 minutes, until the mozzarella has melted and the dish is heated through.
Remove from the oven and serve hot, preferably over cooked fettuccine or spaghetti noodles.