Make Spinach–Artichoke Mixture: In a large bowl, mix together cream cheese, artichoke hearts, garlic, baby spinach, gruyère and Parmesan and season with salt and pepper.
Season chicken with salt and pepper and make a pocket in each breast.
Fill pockets with dip and seal each breast with two toothpicks.
In a large skillet over medium heat, heat oil. Add chicken and cook until deeply golden, 10 minutes per side. Serve immediately.