Preheat the oven to 400 degree F. Heat a large, high-sided, oven-safe skillet over medium-high heat. Sprinkle the skin side of the chicken thighs with salt and pepper. Add the olive oil to the hot pan and place the chicken in the pan, skin-side down. Sprinkle the other side of the chicken with salt and pepper. Let the chicken cook until it easily releases from the pan and is golden brown, about 8 minutes. Flip the chicken and allow to cook for an additional 2 minutes. Remove the chicken to a plate and set aside.
Turn the heat down to medium and add the onion, peppers and red pepper flakes and sprinkle with salt. Let the vegetables cook, stirring regularly, until slightly wilted, about 3 minutes. The natural liquid from the vegetables will help deglaze the pan. Add in the potatoes and garlic and sprinkle with salt and cook, stirring occasionally, for an additional 3 minutes. Add in the tomatoes, vinegar, oregano, thyme and artichoke hearts. Sprinkle with salt and pepper and stir to combine. Turn off the heat and nestle the chicken thighs on top of the vegetables.
Transfer the pan to the oven and bake, uncovered, until the internal temperature of the chicken is 165 degrees F and the potatoes are fork tender, about 35 minutes. Remove the pan from the oven and sprinkle with feta cheese and parsley.