Heat a large skillet over medium-high heat; add the olive oil. Season the chicken with salt and pepper to taste. Lay the chicken skinned side down in the skillet and cook, turning once, until golden, about 4 minutes per side. Transfer the chicken to a baking dish or roasting pan and bake just until firm to the touch, about 10 minutes.
Meanwhile, add the onion, garlic, thyme to the skillet and season with salt and pepper, to taste. Cook, stirring occasionally, until brown, about 5 minutes. Add the artichokes and peppers and cook until brown as well, about 3 minutes. Add the vermouth and stir with a wooden spoon to scrape up the browned bits from the bottom of the pan. Simmer until the vermouth is syrupy, then add the broth and bring the mixture to a full boil. Simmer until the sauce thickens, and season with salt and pepper. Whisk in the butter and add the parsley. Pour the sauce over the chicken, and serve.
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