When President Richard Nixon visited the Vatican in 1970 (at the height of the war in Vietnam), it was decided that the presidential party would leave from St. Peter's Square in an American military helicopter. In order to avoid embarrassing the Curia with unnecessary reminders of the conflict, however, it was suggested that the cigar-chomping secretary of defense Melvin Laird (the brains behind the invasion of Cambodia and the carpet bombing of North Vietnam) should not accompany the rest of the party to the papal audience. Laird, of course, had other ideas...
When the group gathered inside the Vatican, they were surprised to find him loitering about smoking an enormous stogie. He innocently explained that he was merely looking for the president's helicopter. Though he was allowed to stay, Laird was persuaded to pocket his cigar when the pope appeared and began to speak. Unfortunately, it was still alight and Laird's jacket caught fire and began to spew clouds of pungent smoke.
Laird's predicament was partly concealed when he began to frantically slap at his pocket -- prompting many other guests to join in what they mistook to be enthusiastic applause for the pope!
Sources
Little, Brown Book of Anecdotes