A few months ago the picture below came up for sale on Ebay:
The back of the photo is dated March, 1955, and carries the caption: “Valerie Long who is shown here interviewing movie actor Jimmy Stewart on her “Lunch with Val” radio show over station WEAW, will begin a new radio show “Dinner with Val” every Thursday night, from 7 to 7:30 over the same station.” It is also mentioned that the new show will begin on March 10th. Therefore, Stewart must have appeared prior to this date, but the exact date has not been located. In fact, no newspaper reference to this appearance has been found. WEAW is an AM station operating in Chicago, IL.