Apply a thick coat of gel paint stripper to the chair. Liquid paint strippers are thinner than gel ones, they'll run right off vertical surfaces like the seatback and legs and off much of the horizontal area, too. Thicker gel strippers adhere directly to the surface where you apply the product.
Scrape the old paint or stain off the chair with a paint scraper. Depending on the manufacturer, you may leave the stripper on for up to 60 minutes before it begins working. Gently drag the edge of the scraper across the chair, removing the old color.
Sand the wood areas of the chair with 100-grit sandpaper. Wrap the sandpaper around one or two fingers for sanding decorative areas on the chair, gently working the sandpaper over their contours. Give the wood a smooth surface and remove any old paint or stain left on the wood.
Check the chair for signs of cracks or chipping. Tear off a piece of the wood putty, roll it between your fingers and press into damaged areas. Smooth the putty down by rubbing the paint scraper along the top. After the putty dries, gently sand the surface until it blends with the surrounding chair.
Paint the vintage chair with a layer of flat paint if you want a muted shade, or semigloss if you prefer a shiny surface. Apply at least two coats of paint, letting the paint dry between each coat. Depending on the shade you want, you may need more coats.