1. Preheat oven to 425°F. In a medium frying pan, cook chicken, onion, and garlic in olive oil over medium heat, stirring often, until chicken is white, about 10 minutes. Pour off any excess fat. Stir in ricotta cheese, oregano, thyme, salt, hot pepper, and 1/2 cup of marinara sauce. Let cool.
2. Unfold pizza dough and flatten to a 12-inch square. Cut into 4 even squares. Spoon filling into center of each square. Fold dough over filling to form triangles. Press edges together, then crimp with a fork. Make 3 slashes in each calzone to allow steam to escape. Set on a lightly oiled baking sheet.
3. Bake until rich golden brown, about 15 minutes. Heat remaining 1 cup marinara sauce and use as a dip for calzones.