Final answer:
The specific military decoration that can be engraved at government expense is not identified; historically, such engravings signify craftsmanship and honor.
Step-by-step explanation:
The question posed pertains to the area of military traditions and recognitions, more specifically regarding a military decoration that is sponsored by the government in terms of engraving expenses. Historically, engraved items, such as swords, would have the maker's name inscribed as a sign of craftsmanship and recognition. This practice extends to certain military decorations as well. However, with regards to modern U.S. military decorations, the text does not provide enough details to confidently determine which specific award is the only one that may be engraved at Government expense. Traditionally numerous military awards are engraved, and policies can vary with time and between branches of the armed forces.