Preheat the oven to 375°F (190°C).
Prepare the filling by heating olive oil in a skillet over medium heat and sauté the garlic until fragrant.
Add the chopped spinach and oregano to the skillet, cooking until the spinach wilts down, about 3-4 minutes.
Remove the skillet from heat and stir in the crumbled feta cheese, season with salt and pepper to taste.
Carefully butterfly each chicken breast, creating a pocket for stuffing.
Stuff each chicken breast with the spinach and feta mixture, then secure with toothpicks if necessary.
Season the outside of the chicken breasts with salt, pepper, and a sprinkle of oregano.
Place the stuffed chicken breasts in a baking dish and pour chicken broth or wine over the top.
Bake the chicken for 25-30 minutes, or until the chicken reaches an internal temperature of 165°F (74°C).
Remove from oven, let rest for 5 minutes before slicing.