Heat oven to 350°F. Grease large cookie sheet with shortening. In 10-inch skillet, heat oil over medium heat. Add onion and garlic; cook and stir until onion is tender. Reduce heat to low. Add chicken; cook, stirring occasionally, until thoroughly heated.
Separate dough into 8 rectangles; firmly press perforations to seal. Spread about 2 teaspoons of the salsa on each rectangle to within 1/2 inch of edges. Stir 1 cup of the cheese into chicken mixture. Spoon heaping 1/3 cup chicken mixture onto half of each rectangle. Starting with short side topped with chicken, roll up; pinch ends to seal. Place seam side down on cookie sheet.
Bake 16 to 21 minutes or until golden brown. Remove from oven. Top each with about 2 tablespoons of the remaining cheese.
Return to oven; bake 1 to 2 minutes longer or until cheese is melted. Serve with sour cream and additional salsa.