The present invention includes a chain type cutting apparatus for continuous cutting of a rope of a center-filled consumable product into individual pieces, which includes a first continuous elongate rotary chain with a plurality of first open die cavity portions and a second continuous elongate rotary chain with a plurality of second open die cavity portions. The first and second die cavity portions are mutually engageable to form a closed die cavity about a rope of center filled consumable product, forming pieces. The invention incorporates four main variables, dwell time, chain length, chain speed and the number of closed die cavities in simultaneous engagement. These four variables can be altered to increase the output of the product, as well as maintain a satisfactory seal of the center-filled consumable product.