Preheat the oven to 400°F (200°C). Line a cookie sheet with parchment paper.
Unroll the refrigerated pizza dough and roll it vertically into a roughly rectangular shape on the prepared sheet.
In a mixing bowl, combine the chopped cooked chicken, cottage cheese, sour cream, cream cheese, 1 cup of the shredded mozzarella, onion powder, and garlic powder until evenly mixed.
Spread the chicken mixture in a long strip down the center of the dough, leaving about 2–3 inches of dough free at both ends.
Cut 12 even strips on each side of the dough, slanting toward the filling so the strips are roughly equal in width.
Braid the dough by lifting one strip from the left across the filling to the center, then one from the right, alternating until all strips are crossed and ends are sealed.
Bake the braid for 18–20 minutes, or until the dough is lightly browned.
Remove the braid from the oven. Sprinkle the remaining 1/4 cup shredded mozzarella and the French fried onions over the top.
Return to the oven and bake an additional 5 minutes, until the cheese melts. Let cool slightly before slicing and serving.