And here's the back:
With dialogue at the bottom of the photo (Cooper's character is saying, "I don't want you now -- you're not what I thought..."), a practice not uncommon at Paramount in the early 1930s, one would think this picture's prime use was in theaters, where it could serve as sort of a lobby card. And maybe it was. But it found its way to other places, as a closeup of part of the back makes evident:
It reads "LIBERTY ART. DEPT.", almost certainly referring to Liberty magazine. We see the notation "LOMBARD," along with "Feb. 28" and (page) "28." But look to the end of the second line, and you can make out a "1942" on the stamp. Evidently this photo was used, or at least considered, for use in Adela Rogers St. Johns' two-part tribute to Carole several weeks after her passing (http://community.livejournal.com/carole_and_co/174086.html and http://community.livejournal.com/carole_and_co/174533.html).
This photo is being auctioned at eBay.-- and as I said earlier, you don't have much time; bidding closes at 8:25 p.m. (Eastern) tonight. Two bids have been placed as of this writing, with the high bid at $27.
If interested, go to http://cgi.ebay.com/Photo-Carole-Lombard-Gary-Cooper-AAJ039_W0QQitemZ270423185966QQcmdZViewItemQQptZLH_DefaultDomain_0?hash=item3ef67a5a2e&_trksid=p3286.c0.m14&_trkparms=65%3A1%7C66%3A2%7C39%3A1%7C293%3A1%7C294%3A50.