Preheat the oven to 300 degrees F.
In a large Dutch oven, in 2 tablespoons of olive oil, sauté the onion for 2-3 minutes stirring occasionally, with the salt. Add the fennel slices and continue stirring until the onion is golden and mostly cooked. Add the garlic and stir the pot a few times before removing the vegetable mixture to a small plate.
In another tablespoon of olive oil, brown the chicken over high heat, for 4-5 minutes, turning once to brown the other side. Remove the chicken to a plate.
Add the ½ tablespoon of butter and ½ tablespoon of olive oil and brown the mushroom quarters quickly over high heat. Remove to another small plate.
Add the tomatoes, sprinkle the crushed basil over, sautéing for a minute while stirring. Add the wine and deglaze the pan, being sure to stir the bottom well. Then stir in the chicken broth. Next add the paprika and saffron and stir. Add back in to the pot, the chicken, onion and fennel medley, mushrooms, and artichoke hearts. Squeeze the lemon juice over the ingredients.
Cover and cook at 300 degrees for approximately 1 ½ hours (or 1 hour, 20 minutes). Chicken will be very tender. Add the olives during the last 10-15 minutes of cooking. Remove the cover before returning to the oven to finish cooking.
Remove from the oven. Serve over a bed of brown rice or white rice. Garnish with a bit of chopped Italian parsley if you like. And serve with small lemon wedges or spritz the top of the dish with lemon after cooking.