In a large skillet, heat 2 tablespoons olive oil over medium heat. Season the chicken with salt, place in the skillet skin side down and cook until golden-brown, about 7 minutes on each side; transfer to a plate. Reserve the skillet.
Meanwhile, in a medium pot of boiling salted water, cook the orzo until al dente, about 5 minutes. Add the artichokes and cook for 2 minutes. Drain and add the remaining 2 tablespoons olive oil and 3 tablespoons dill.
In the reserved skillet, cook the onion and garlic in the chicken drippings over medium heat until softened, 7 minutes. Add the wine, chicken broth and cherry peppers and boil until reduced by half, about 3 minutes. Add the remaining dill and hot pepper liquid. Return the chicken to the skillet and simmer until heated through, 1 minute. Transfer the orzo to a platter and top with the chicken and sauce.