Preheat the oven to 400°F.
Place the frozen spinach in a kitchen towel and wring out as much liquid as possible. Transfer the spinach to a medium bowl then stir in the mozzarella cheese, cream cheese, chives, garlic powder, paprika, 1/2 teaspoon kosher salt and 1/4 teaspoon black pepper.
Using a sharp knife, cut a deep pocket lengthwise into each chicken breast without cutting all the way through.
Divide the filling among the chicken breasts, tucking it securely inside each pocket. Use toothpicks to secure the pockets shut.
Season the outside of the chicken breasts with salt and pepper (and any other preferred seasonings).
Add 2 tablespoons olive oil to two separate large, ovenproof skillets set over medium heat. Once the oil is hot, add two chicken breasts to each pan. Brown the chicken breasts on one side then flip them once and brown the second side for an additional 3 minutes.
Transfer the skillets into the oven and continue cooking the chicken breasts until they reach an internal temperature of 165°F, 10 to 15 minutes.
Remove the chicken breasts from the oven and let them cool slightly before removing the toothpicks and serving.