I spotted this chair on the French site, Interieurs, in the video "Deco Ethnique." That small amount of pink-and-yellow ikat fabric used just for the back, as well as for the welt on the arms and seat, gives the Louis XV chair so much punch. (Ikat is an Indonesian word for a fabric dyeing process.)
It would be fun to reinvent a vintage chair using a remnant of ikat -- ideally a pattern from Robert Kime or Madeline Weinrib's "Turquoise Luce," shown below. But economically priced silk-cotton ikats in luscious colors can be found on eBay and at Uzbek Craft. Although Uzbek Craft offers wholesale prices, all items ship from the Republic of Uzbekistan, so double-check shipping costs to the U.S. and inquire about the exact dimensions of available ikats.
Lewis Sheron, based in Atlanta, has an ikat-like pattern, "Santana," below. It costs $13.98 per yard and can be found online under Fabric, Contemporary. Swatches cost about $2.50.
The Fabric of Life
Ikat: Splendid Silks of Central Asia from the Guido Goldman Collection
Ikat: Splendid Silks of Central Asia
Above, Kelly Wearstler upholstered a chair with ikat in her Hillcrest library, as seen in Domicilium Decoratus.