Why are the chiefs' quarters known as the goat locker?

This is the space where the Chief Petty Officers, the highest-ranking enlisted men, sleep. The space is so named because the chiefs are the “old goats” in the Navy. On a submarine in WW2, they were as “old” as 28 or 30 years old. 

In this case, goat is not necessarily GOAT, as in greatest of all time. Nor does it imply that the chiefs smelled more like goats than the rest of us. After a few days at sea, we all smelled pretty bad.

The chiefs’ quarters are known as the goat locker throughout the Navy, not just on submarines.