It was not the closest the US and USSR came to blows during the Cold War, but the Turkish Straits crisis of 1946 was both the first and easily the most thoroughly forgotten brush with World War III.
Briefly, at the end of World War II the Soviets under Stalin made a laudably ballsy attempt to solve one of its oldest strategic, economic, and political handicaps. For all its globe-spanning size, neither today's Russia or the former USSR lacks one very basic and crucial feature: a year-around ice free shipping port. Its eastern ports are not economically and militarily useful because they are thousands of miles from European Russia, and its northern ports like Murmansk and Leningrad / St. Petersburg (Not to be confused with the one in Florida, aka "America's Strip Club") freeze over during the winter.
Of course the country has port access in other places, but all involve a second country. Most prominently, the Black Sea provides year-around access to the Mediterranean (and thus the world) but requires passage through two narrow straits that pass through Turkey – the Bosphorous and the ones I have never once spelled correctly on the first try, the Dardanelles. If you recall, two years ago we refreshed our memories about how important this Black Sea outlet to the world is to the Russians when they moved aggressively into Ukraine to secure access via the Crimea. There was also a thing called the Crimean War a while back. It's safe to say this is kind of a big thing to Russia. (As a side note, Soviet Georgia had territorial claims on part of Turkey, which the Russian government includes today in their territorial claim over, well, all of its former republics)
In the period of exhaustion and confusion that followed WWII, the Soviets formally demanded that Turkey allow it to place bases on the Bosphorus and the Dardanelles. Later the demand evolved to joint Soviet-Turkish administration of the straits, effectively giving the USSR not only access to but sovereignty over the seaway. Harry Truman, always one for subtlety, used the pretense of needing to repatriate the remains of the recently deceased Turkish ambassador to the US to send the battleship USS Missouri and a half-dozen other Big Stick vessels to Turkey to sail around and look really impressive. The Soviets responded by conducting "exercises" in the Black Sea within spitting distance of the Turkish shores. In a then-classified telegram, American diplomat Dean Acheson described the situation in a way that would come to define the Cold War:
In our opinion the primary objective of the Soviet Union is to obtain control over Turkey. We believe that if the Soviet Union succeeds in introducing into Turkey armed forces with the ostensible purpose of enforcing the joint control of the Straits, the Soviet Union will use these forces in order to obtain control over Turkey…. In our opinion, therefore, the time has come when we must decide that we shall resist with all means at our disposal any Soviet aggression and in particular, because the case of Turkey would be so clear, any Soviet aggression against Turkey. In carrying this policy our words and acts will only carry conviction to the Soviet Union if they are formulated against the background of an inner conviction and determination on our part that we cannot permit Turkey to become the object of Soviet aggression.
Even Stalin, as belligerent as they come, recognized that the Russians were not actually prepared to fight over the straits or anything else in the Summer of 1946. The USSR dropped its formal request to take possession of the two straits but, for face-saving purposes, maintained its "opinion" that the Soviets should have sovereignty over them. When Stalin died they abandoned the issue altogether. By then it was too late, though. The acquisitive stares and saber-rattlings of the Soviet Union sent Turkey running for the sweet protective embrace of NATO and $100,000,000 in economic aid in 1952.
As the story of the assassination of the Russian ambassador to Turkey unfolds, it's worth keeping in mind that successive Russian governments have been searching for a reason to fight this fight for a couple of centuries. It's a good thing we have such a strong visionary leader ready to stand up against Russian aggression. A modern day Harry Truman.