The correct answer is C) master. According to maritime regulations, each completed page of the Oil Record Book must be signed by the master (captain) of the vessel. This requirement is specified in Annex I of the International Convention for the Prevention of Pollution from Ships (MARPOL), which governs the handling and disposal of oil and oily waste on ships. The master is responsible for ensuring that the Oil Record Book is properly maintained and that all entries are accurate, making their signature a necessary part of the record-keeping process. The other options (chief mate, chief engineer, engineer on watch) are incorrect because they are not the designated signatories for the Oil Record Book under MARPOL regulations.