Steam has at last triumphed in the air; the successful flights that have taken place at Oakland in California have prove beyond the shadow of doubt that steam is destined to play a most important part in the history of aeronautics. It is little to be wondered at that experts are watching the progress of this invention of the Besler Brothers with keen interest, when one realizes what it means to Aviation to possess a silent plane capable of being started up by simply closing a switch in front of the pilot, which without any other effort or thought on his part, starts the burner, appraises the required working pressure of steam in the generator, in the space of thirty seconds or so, sufficient to send the airscrew whirling at 1,625 revolutions per minute. [source]
In April of 1933 two brothers, George and William Bresler, demonstrated the first successful flight of a steam powered airplane. The airplane was a Travel Air 2000 that was modified by the addition of a 2 cylinder steam engine. Above is a newsreel recording that day.
They made several takeoffs and landings during the demonstration. What impressed spectators the most was the silence of the airplane. That was an important selling point, because in those days before radar planes were located and tracked acoustically.
Here are two 1933 articles about the plane from Popular Science and Scientific American which include more details, as well as photographs and diagrams of the plane and its engine. The above quote's source link also has a number of articles, diagrams and pictures.