Polar Bear Patch worn by USMC 1st Marine Brigade (Provisional) in Iceland in 1941-42.  It was the patch worn by the British forces the Marines were sent to reinforce.  I believe this represents the USA's first official military action in support of the war against Nazi Germany. 

The Marines wore the patch in solidarity with the Brits, having gained permission from HQMC to wear another country's insignia. 

This is a photo of one of the patches worn by then- 2nd Lt.  Donald B Cooley, Jr.

On 7-July, 1941, a convoy of US Navy ships and civilian transports arrived at the port of Reykjavik carrying The 1st Marine Brigade (Provisional) under Brigadier General John Marston.  These Marines had been dispatched to Iceland by FDR, at the request of Winston Churchill, to assist in defense of the island and its critical weather station which supplied advance weather information to British Commonwealth nations fighting the Nazis. 

https://en.wikipedia.org/wiki/British_Empire_in_World_War_II

Enroute from Newfoundland the US convoy passed through the flotsam and jetsam of the British battleship HMS Hood, which had been sunk by the German pocket battleship Bismarck on 24 May. The Bismarck's sister ship Tirpitz was known to be patrolling the N. Atlantic at the time. 

To the best of my knowledge, this was the earliest involvement of US forces in the fight against Hitler's Nazi forces, five months prior to the attack on Pearl Harbor.  They did not see any combat, or hostile action of any kind, save periodic overflights of German reconnaissance planes.  Dad told of spotting a plane approaching once when standing watch with binoculars, running through in his head the various profiles he had learned just a few months earlier in USMC officers basic school, and doing a double-take when he recognized a Heinkel.  I believe it was probably an HE-115which had sufficient range to have made the round-trip from Europe to Iceland. 

The Marines and the British formed a strong alliance.  Since the US was not in the war, the Marines could not officially report to the British commander.  Both sides agreed to a special peer-level cooperative arrangement.  When British Major General Henry O. Curtis, commander of the British force's 49th Division, suggested that the 1st Brigade wear the 49th's Polar Bear shoulder patch, General Marston agreed, after receiving the go-ahead from HQMC to wear the insignia of the partner nation.  The Marines wore the patch with pride. 

Dad saved three Polar Bear Patches along with his various campaign medals and insignia.  He was in the 5th Defense Battalion.  Page 12 describes the battalion's arms and deployment.  It mentions they had three highly secret radar sets, the first ever employed by Marines in the field.  Dad said they were not allowed to discuss them, not even say the word.  When any mention of them was necessary, they were referred to as "the hush-hush". 

We Cooleys have been engaged in supporting the fight against Naziism for over 76 years.  Not stopping now. 

Yanks helped the Brits then; they and the Canucks, Kiwis and Aussies are helping us now - FVEY