Ok- it looks like the elk horn chair Seth Kinman gave to President Lincoln made the photo studio rounds in 1864. I now have a copy of the Brady version of the chair’s portrait, along with the Alexander Gardner version. In perusing the Wikipedia article, there appears to be at least one other Brady version of the Kinman-Lincoln chair. I’m trying to find out the disposition of the chair today – it may be part of the White House collections, or it may belong to the Smithsonian. I’ll update when I find out.
According to Wikipedia, here is the story of this particular chair:
Kinman’s presentation of an elkhorn chair to President Abraham Lincoln at 10 a.m. on Saturday, November 26, 1864 was recorded by artist Alfred Waud, the only known picture of Lincoln accepting a gift. The drawing shows Lincoln examining Kinman’s rifle, which he called “Ol’ Cottonblossum.” Kinman also presented a fiddle made from the skull and a rib of his favorite mule and played the instrument.
Much to the amusement of Lincoln and other spectators, he played ‘Essence of Old Virginia’ and ‘John Brown’ on the bones of the mule. Lincoln said that if he could play the fiddle he would ask him for it, but since he could not, the fiddle would be better off in Mr. Kinman’s hands.
Within three weeks, Lincoln stated that he would prefer to eat Kinman’s chair, antlers and all, than to appoint a certain office-seeker.
The following April, Kinman marched in President Lincoln’s funeral cortege in Washington.

Here is the Gardner CDV for comparison:

To quote the Wikipedia page about Seth Kinman:
Seth Kinman (September 29, 1815 – February 24, 1888) was an early settler of Humboldt County, California, a hunter based in Fort Humboldt, a famous chair maker, and a nationally recognized entertainer. He stood over 6 ft (1.83 m) tall and was known for his hunting prowess and his brutality toward bears and Indians. Kinman claimed to have shot a total of over 800 grizzly bears, and, in a single month, over 50 elk. He was also a hotel keeper, barkeeper, and a musician who performed for President Lincoln on a fiddle made from the skull of a mule.
Known for his publicity seeking, Kinman appeared as a stereotypical mountain man dressed in buckskins on the U.S. east coast and selling cartes de visites of himself and his famous chairs. The chairs were made from elkhorns and grizzly bear skins and given to U.S. Presidents. Presidents so honored include James Buchanan, Abraham Lincoln, Andrew Johnson, and Rutherford Hayes. He may have had a special relationship with President Lincoln, appearing in at least two of Lincoln’s funeral corteges, and claiming to have witnessed Lincoln’s assassination.
His autobiography, dictated to a scribe in 1876, was first published in 2010 and is noted for putting “the entertainment value of a story ahead of the strict facts.” His descriptions of events change with his retelling of them. Contemporary journalists and modern writers were clearly aware of the stories contained in the autobiography, “but each chooses which version to accept.