Using a sharp knife, carefully cut a deep pocket lengthwise into each chicken breast without cutting all the way through to the other side.
In a medium bowl, mix all ingredients for the marinade: 2 tablespoon olive oil, lemon juice, oregano, 1/2 tsp salt, and 1/2 tsp pepper. Add the chicken and stir to coat. Cover and let site in the fridge for at least 15 minutes and up to one hour.
Heat 1 tsp oil in a sauté pan, over medium heat. Add spinach and cook for 5 minutes, stirring often, until the spinach is softened. Turn off heat, add both cheeses and a pinch each of salt and pepper.
Preheat oven to 400 degrees Fahrenheit.
Remove chicken from marinade and divide spinach mixture into each chicken breast, stuffing deep into each pocket.
In an oven safe sauté pan, over medium heat, heat 1 tablespoon of oil. Add chicken breasts and sear for 5 minutes, until chicken is golden brown. Carefully flip chicken breasts, without pushing out filling, and cook another 3 minutes on the other side.
Turn off heat and transfer to the the oven. If you do not have an oven safe pan, you can transfer the chicken to an oiled baking sheet before putting in the oven.
Bake chicken for 10-20 minutes or until thermometer reads 165 degrees Fahrenheit. Cooking time will de dependent on the size of your chicken breast. My chicken was smaller and only cooked for about 10 minutes.