Heat the oil a medium straight-sided skillet over medium-high heat. Dry the chicken breasts well and sprinkle evenly with the salt. Place the breasts skin-side down in the hot pan and cook undisturbed until deep golden brown, about 6 minutes. Using tongs, flip the chicken to the bone side and continue to cook for another 5 minutes. Remove to a plate while you build the sauce.
In the same pan, add the shallots and sweat, stirring occasionally, for a minute. Add the preserved lemon, olives and sun-dried tomatoes and stir to combine. Deglaze with the white wine, scraping up the brown bits from the bottom of the pan with a wooden spoon. Simmer for 3 minutes to reduce slightly. Add the chicken broth and return to a simmer. Add the oregano and the chicken back to the sauce. Spoon some of the liquid over the chicken. Cover the pan and simmer gently until an instant-read thermometer registers 160 degrees F, about 25 minutes. Allow the chicken to rest in the sauce for 10 minutes. Stir in the parsley.
Serve the chicken with a generous helping of the sauce and sprinkled with chive blossoms if using.