Heat olive oil in a large, heavy-bottomed, oven-safe skillet over medium-high heat. Remove the chicken thighs from the marinade, discarding the zip-lock bag and any leftover marinade. Place the chicken in the skillet, skin-side down, and cook until golden brown, approximately 5 minutes. Flip the chicken over and cook the other side for an additional 4-5 minutes more.
Remove the chicken from the skillet and transfer to a clean plate. The chicken will not be fully cooked, that's ok.
Pour off any excess fat left behind in the pan and carefully scrape off any burnt bits stuck to the bottom of the skillet with a scrunched up, slightly damp, paper towel. If the burnt bits do not come off, you may clean the skillet (see note 2).
Return the skillet to the stove. Add the remaining 1 tablespoon of olive oil to the skillet over medium-high heat. Add the diced onion and sauté for 4-5 minutes, or until translucent. Add the garlic, dried Italian seasoning, oregano, salt, and rice to the skillet and mix well to combine with the onion. Cook, stirring continuously, for 2-3 minutes.
Add the green olives, artichoke hearts, low-sodium chicken broth, and lemon juice to the rice and stir to combine. Bring rice to a simmer and place the chicken on top. Preheat oven to 350 Degree F.
Remove from heat and cover the skillet with a lid, baking sheet, or piece of foil. Transfer to the oven to cook for 30 minutes covered, plus an additional 15 minutes uncovered, or until the rice has absorbed all liquid and chicken is fully cooked.
Remove from the oven and allow your chicken and rice to cool for 5-10 minutes. Garnish with fresh chopped parsley and oregano and serve with herbed olives and feta (see below). Enjoy!