The three Allied leaders met at the Soviet Embassy, which was across the street from the British Embassy. FDR was staying at the Soviet Embassy to avoid the necessity of being driven to the site each day from the American Embassy, more than a mile away, possibly exposing himself to attack. The story is that Hitler assigned Otto Skorzeny, the SS officer best known for freeing Mussolini from captivity in July 1943, to lead an effort to kill the Big Three during their meeting. Before any attempt was made, however, the Soviets got wind of it, and the plot was called off.
In the mid-1960s, Laslo Havas, a Hungarian, published a book about the supposed plot, Hitler's Plot to Kill the Big Three. Much of the information available about the plot, code-named Operation Long Jump, seems to come from that book and Russian sources.
Gary Kern, writing for the CIA's Studies in Intelligence, vol. 47, No. 1, 2003, is skeptical about the whole thing, and posits that Stalin and his men concocted the tale, which was later embellished by the KBG to glorify the skill of Soviet intelligence, which was credited with thwarting the plot. "... the NKVD retained the story of the plot and, twenty years later during a publicity campaign, its successor, the KGB, began to promote it in the press," Kern wrote.
"In its new guise, the purported plot against FDR acquired a wealth of details and a sterling cast of characters, most notably SS Capt. Otto Skorzeny, one of the legendary figures of World War II. In the literature generated by the KGB, Skorzeny was the man designated by Hitler to lead the attack on the Big Three in Tehran and, in one stroke, turn the war around. But — the story went — the Nazis did not count on NKVD ace Nikolai Kuznetsov, who, posing as a Wehrmacht lieutenant in occupied Ukraine, befriended a hard-drinking and talkative SS officer named von Ortel, who blurted out revealing tidbits of the plan... As might be expected, Skorzeny’s memoirs mention no such plan and the various Soviet accounts differ among themselves in names, places, and other specifics.
"In fact, a Georgian defector who claims to have heard the inside story from sources close to Stalin and Beria (both Georgians), debunks the idea of a Nazi plot. In order to impress Roosevelt and impose a feeling of indebtedness on him, writes Yuri Krotkov (a pseudonym), Stalin conceived a bogus assassination attempt and ordered Beria to set it up, with the provision that 'assassins' should actually be arrested..."
"Although the evidence remains insubstantial, it is not altogether impossible that the Nazis did plan an attack on the Allied leaders, perhaps even at the Tehran conference and even with only a week to prepare. It is completely impossible, however, that such a Nazi plan could have been the one that Stalin warned FDR about. If Stalin thought that Otto Skorzeny, who had whisked Mussolini off a mountain top as if he were a feather, were planning to assassinate him, or to try any action in Tehran, he would have postponed the conference and left. He would not have remained in the city even if the story that his own men were spreading were true, that a half-dozen assassins possibly capable of shelling the Soviet Embassy were in the vicinity. He was not a man to take such a risk."
Kern's entire article, "How 'Uncle Joe' Bugged FDR" is here, covering a lot more ground than Operation Long Jump.