§1. Every priest and a priest alone validly administers the anointing of the sick.
§2. All priests to whom the care of souls has been entrusted have the duty and right of administering the anointing of the sick for the faithful entrusted to their pastoral office. For a reasonable cause, any other priest can administer this sacrament with at least the presumed consent of the priest mentioned above.
§3. Any priest is permitted to carry blessed oil with him so that he is able to administer the sacrament of the anointing of the sick in a case of necessity.
Source: Code of Canon Law (Vatican.va)