In a medium skillet, melt butter over medium-high heat. Add spinach and artichoke and saute 3-4 minutes, stirring occasionally until spinach is wilted. Add garlic and saute 1 additional minute until fragrant. Season with salt and pepper to taste and allow spinach mixture to cool slightly.
Meanwhile, in a small bowl, combine cream cheese, mozzarella, and Parmesan until smooth. Set aside for a moment.
Using a sharp knife, cut 6 even slits in each chicken breast about 3/4 of the way through (do not cut all the way through) Season chicken breasts with salt and pepper, place in a 9x13 baking dish, and preheat oven to 375F.
Combine cream cheese mixture and cooled spinach mixture. Fill the cut chicken slits with mixture. Bake chicken at 375F 20-25 minutes until chicken registers 165F. If desired, broil chicken under high heat 1-2 minutes to brown cheese. Serve chicken hot and enjoy!