Apparatus grips and pulls zipper chain along from supply to a desired finite length, installing slider on the way. When next gap in chain is detected by a finger which inserts itself into gap and abruptly stops further advance of tape, a cutter closes to cut chain to length. Puller is driven by air cylinder, and back pressure is applied soon after puller starts. This reduces pulling force and eliminates tearing of zipper tape as tape is abruptly stopped.