Final answer:
The Medal of Honor is the only military decoration that may be engraved at Government expense. It's awarded for acts of valor and comes with several privileges, including government-funded personalized engraving.
Step-by-step explanation:
The only military decoration which may be engraved at Government expense is the Medal of Honor. This recognition is the highest and most prestigious personal military decoration that may be awarded to recognize U.S. military service members who have distinguished themselves by acts of valor. The Medal of Honor is one of the most revered and respected medals in the military, and recipients are given several privileges, including a special pension, invitation to all future presidential inaugurations, and, relevant to the question, personalized engraving paid for by the government.