Nice example of a scarce piece of WWI-era headgear, a USMC rubberized rain cap. Has a 1917 contract stamp on the interior.
This one has a hole and marks of having had an EGA, it didn't have one but I displayed it with one for a while and then gifted the EGA to a friend.
I haven't seen photos of these being worn in France, they are somewhat of an anomaly but an attractive piece of WWI-era Marine Corps headgear.