The correct answer is A) windlass. The windlass is the machinery associated with heaving in and running out anchor chain on a vessel. The windlass is a deck-mounted machine that uses a rotating drum and gears to haul in and pay out the anchor chain, allowing the crew to control the deployment and retrieval of the anchor. The other answer choices are incorrect because: B) draw works is associated with oil drilling rigs, not anchor handling; C) dynamic pay out system refers to specialized equipment used for deep-sea mooring, not typical anchor windlass operation; and D) winch is a more general term that could refer to various hoisting or pulling machinery, but does not specifically describe the anchor chain handling equipment.