Pat your chicken dry with paper towels to promote browning. In a small bowl, mix the dried oregano, paprika, cayenne pepper, salt, and black pepper. Rub this spice blend evenly all over the chicken breasts or thighs.
Heat the extra virgin olive oil in your large skillet over medium-high heat. Add the chicken and sear for about 3-4 minutes on each side until golden brown but not fully cooked through. Remove the chicken and set aside.
Reduce the heat to medium and add butter to the skillet. Once melted, toss in the sliced shallots and chopped garlic. Sauté until fragrant and translucent, about 2-3 minutes. Add the orzo and rice, stirring frequently to toast the orzo lightly (about 1-2 minutes).
Pour in 3 cups of low sodium chicken broth along with the lemon juice. Stir to combine, scraping any browned bits from the bottom of the skillet. Nestle the chicken pieces back into the pan and scatter lemon slices on top.
Cover the skillet with a lid and reduce the heat to low. Let everything simmer gently for 18-20 minutes or until the rice is fully cooked and has absorbed most of the liquid. Add more broth if needed to keep the rice moist.
Once the rice is tender, stir in the chopped spinach and crushed green olives. The spinach will wilt quickly in the residual heat. Turn off the heat and sprinkle crumbled feta cheese and fresh basil leaves over the top.
Serve your One Skillet Greek Lemon Chicken and Rice hot, garnished with extra lemon wedges if desired. This meal pairs beautifully with a simple cucumber salad or warm pita bread.