"All Is Vanity" - While the Enterprise is orbiting Earth, the crew – Kirk, Spock, McCoy, Scotty, Chekov, Sulu, Uhura and Chapel - intends to beam down for shore leave. Only to end up in an alternate late 1940s Chicago, where Al Capone became the President in 1936 and in the midst of running for his fourth term. In Al Capone’s America, there are positives in that the interment camps were never created and the hate groups were purged all across America, thanks to the mob. But the country has never really recovered from the Great Depression, and lost the war in the Pacific, with Imperial Japan annexing the American territories, including Hawaii. And it never entered the war in Europe, allowing Nazi Germany to develop nuclear technology and overwhelm the continent when it was used with the V2 rockets. When Capone, Kirk and the rest of the crew, receive word that both Imperial Japan and Nazi Germany have attacked America simultaneously – air raids all across California and V2 rocket attacks all along the Eastern seaboard - Capone begs Kirk to use his starship to help him. But Kirk just wants to get his crew back to their timeline, and hopes his crew on the Enterprise figure out what happened to them.
(basically I fused two unused TOS ideas together, Imperial Japan winning WW2 and President Capone, for a story)
Next episode - "When the Walls Came Tumbling Down"