Begin by heating the olive oil in a large skillet over medium heat. Season the chicken breasts with salt, pepper, and dried oregano on both sides.
Place the chicken in the skillet and cook for approximately 6-7 minutes on each side, or until the chicken is cooked through and has a golden crust. Remove the chicken from the skillet and set aside.
In the same skillet, add the minced garlic and sauté for about 1 minute until fragrant.
Lower the heat and add the cream cheese and Greek yogurt to the skillet, stirring until they melt together into a creamy sauce.
Mix in the chopped spinach and artichoke hearts, stirring until the spinach wilts, and everything is well combined.
Add the mozzarella and Parmesan cheese to the skillet, mixing until the cheeses are melted and the sauce is creamy.
Return the cooked chicken breasts to the skillet, spooning the creamy mixture over them. Let it cook for an additional 2-3 minutes to heat the chicken through.
Season with additional salt and pepper if needed, and garnish with fresh parsley before serving.