The photo is dated Feb. 5, 1937, and the man with Clark and Carole is named Irvin S. Cobb. Few remember him today, but in the 1930s he was a well-known writer and humorist who also dabbled in movie writing and acting. He was a close friend of Will Rogers, and hosted the Academy Awards in 1935.
At what event was this taken? I have a feeling it was a benefit for the Red Cross at the Shrine Auditorium in Los Angeles, as there's a photo datemarked Feb. 4 showing Gable and Lombard in much the same outfit, although this pic has Clark showing his support for the Shriners:
The Gable/Lombard/Cobb photo is "an original Type I wire news press Acme photo . Photo measures 8x5. This is part of a collection from a former employee of the UPI in Tribune Towers [Chicago] before this collection was moved to New York."
The photo currently has one bid on it, for $9.99; bidding ends at 10:25 p.m. (Eastern) Wednesday. If you're interested in owning it, or simply want to learn more, go to http://cgi.ebay.com/1937-Clark-Gable-Carole-Lombard-Irving-Cobb-Wire-Photo-/170530949093?pt=Art_Photo_Images&hash=item27b46fc7e5.