Preheat a skillet or grill pan over medium heat and add olive oil.
In a bowl, mix together the shredded chicken, mozzarella cheese, cheddar cheese, cream cheese, minced garlic, parsley, salt, and pepper until well combined.
Divide the chicken and cheese mixture evenly among the low-carb tortillas. Roll each tortilla tightly to form wraps.
Place the wraps seam side down in the preheated skillet. Cook each wrap for 2-3 minutes per side, or until the wraps are golden brown and the cheese is melted.
Remove from skillet, slice in half, and serve hot. Garnish with extra parsley if desired.
