Season the chicken pieces with salt, oregano, thyme, rosemary, and black pepper.
Heat the olive oil in a large non-stick (recommended) skillet over medium heat. When the oil is hot but not smoking, add the chicken in a single layer. Cook for 3 minutes without disturbing.
Turn the chicken pieces and cook for another 3 minutes. (Use a spatula to get under sections of chicken and flip several pieces at once.)
Add the garlic and cook for 1 minute, stirring often.
Carefully add the white wine. Cook for 2 minutes, stirring occasionally.
Add the chicken broth, lemon juice, artichokes, and tomatoes. Stir well to combine.
Let the liquid come to a simmer. Lower the heat to medium-low, cover, and cook for 10–15 minutes or until the chicken is cooked through (internal temperature should reach at least 165°F in the thickest piece). Stir occasionally.
Add the butter and stir until it melts. Turn off the heat.
Taste the sauce and add more salt, if needed. (As a reference, we added ¼ teaspoon to ours.)
Garnish with chopped parsley and serve with Parmesan cheese, if desired. Serve with pasta, rice, or a generous piece of bread for dipping.