Through examining both the front and back, we determined the photo was taken for Selznick-International Pictures, a studio for whom Carole made two films. But which one was this for -- "Nothing Sacred" (my guess) or "Made For Each Other"? Doug, a regular contributor to this community, writes that it was indeed "Nothing Sacred":
"Yes, that is the exact outfit Carole wears about 2/3rds of the way through the film when she is honored at a 'live' show, makes an appearance onstage, and collapses from too much liquor (although the crowd believes it's the effects from radiation). In Technicolor, it's blue, I believe (or at least in the blue family)."
As it happens, I have some color captures from "Nothing Sacred," and they confirm it is indeed that dress -- and Doug is right when he says it's "in the blue family." Just how blue is hard to say, as "Nothing Sacred" has been in the public domain for decades, and there are thus many subpar prints of the film in circulation, many of which were used as is for video and DVD release.
Having Lombard in blue (a dress designed by Travis Banton, familiar with Carole's form from their several years at Paramount; he also dyed the furs she was wearing a similar shade) was deemed sort of a technical wonder at the time, since three-strip Technicolor hadn't been perfected until a few years before "Nothing Sacred" was released in November 1937. (Before that, blue was virtually impossible to photograph accurately, which is why so many two-strip Technicolor films emphasize reds and greens.)
So here's that dress, worn so colorfully by Carole:
The UCLA film archive has restored "Nothing Sacred," but I'm not sure if a DVD version of this print has been issued; perhaps that's the print Film Forum in New York will use Nov. 28 and 29 when it shows the movie as part of its Lombard festival (http://community.livejournal.com/carole_and_co/148639.html). It likely would provide us the precise shade of blue Carole is draped in.