Roll each dinner roll into a strip 2 1/2 inches wide by 10 inches long. Spread about 2 tablespoons Alfredo sauce onto each strip. Sprinkle each one with oregano and garlic salt. Divide chicken equally and place on the strips. Top with about 3 tablespoons of cheese on each strip.
Roll up the dough about two thirds of the way. Lift the other end over and seal the dough slightly. Carefully lift each roll up and place in a sprayed 8x8 inch baking pan in three rows of three with the sealed end down. Cover with remaining Alfredo sauce and sprinkle with remaining cheese.
Bake at 350°F 35-40 minutes. Cover with foil last 10 minutes to prevent over browning if necessary.