One inspiration for their current work, the gallery says, is medieval tapestry.
The gallery says it is doing so in light of "ongoing military actions across the globe."
Nevertheless, curators and international galleries say there is growing interest here.
The form of "Die" was inspired by an index card file, the gallery said.
"I love hearing people in the galleries saying the Frick is a much better place but that nothing has changed," he said.
The gallery originally said it expected the expansion to cost $40 million.
The gallery would not say how much the painting is worth.
There are more than 2,000 drawings in all, each one unique, the gallery says.
The 15-by-18-inch painting has not been seen publicly for 29 years, the gallery says.
The gallery, which is selling the chair for $5,500, says it is not French.