Move the chair to a well-ventilated area. Place a tarp over the work area and place the chair on top of the tarp to catch excess chemicals and dust from sanding.
Apply the chemical stripper evenly to the entire stained surface of the chair with a paintbrush. Wait a few minutes for the stripper to take effect. When it does, the stained surfaces of the chair begin to bubble and blister. Once the entire surface has blistered, gently use a flat metal scraper to scrape away all of the blistered areas of stain. Continue scraping the entire surface until most or all of the stain has been scraped away.
Scrape away any excess stain around corners and detailed areas of the chair with a steel wool pad until all of the blistered stain has been removed. Wipe down the entire surface of the chair with a clean rag. Continue wiping the chair down until all of the debris is gone.
Apply a generous amount of paint thinner to the wooden surface of the chair with a rag or paintbrush. The paint thinner will finish stripping the wood and make it easier to sand the wooden surface. Wait a few minutes for the paint thinner to absorb into the surface of the wood and dry completely.
Sand the wooden surface of the chair with the 120-grit sandpaper first to remove any leftover stain and any rough edges. Sand the wooden surface of the chair with the 220-grit sandpaper to completely smooth the surface of the wood. Wipe down the entire surface of the chair with a clean rag.
Apply the new stain with a paintbrush, beginning at the top of the chair. Make even strokes with the paintbrush to evenly apply the stain. Continue staining the wooden surface of the chair from the top of the chair to the bottom. Once you have reached the bottom of the chair, let the new stain dry for at least 12 hours.
Inspect the chair for any missed areas after the stain has completely dried. Stain the missed areas as needed with the stain and a paintbrush. If the stain color is not dark enough, continue applying more stain to the chair until the desired color has been reached. Wait another 12 hours for the stain to dry completely.
Apply a thin layer of shellac over the stain once it has completely dried. Use a clean paintbrush to apply a thin, even layer of shellac over the stained surface of the chair. The shellac will make the stain shine. Wait 30 minutes for the shellac to dry and apply more shellac as needed to reach the desired shine.