Place a drop cloth over your work area, which should be well ventilated but safe from sudden drafts.
Put on your gloves and face mask. Using a paintbrush, apply stripping agent to the cedar chest. Do not paint the stripping agent back and forth as you would with paint. The stripping agent works best when it is thickly applied. Let the stripping agent set for the period of time recommended by the manufacturer.
Wipe off the stripping agent with rags after it has set for the recommended period of time. Inspect the chest and repeat Steps 2 and 3 if most of the old finish has not already been removed.
Sand the cedar chest using medium-grit sandpaper. Do not over-sand any area. Keep all surfaces as close as possible to the original texture and grain of the wood.
Sand the chest again, this time with fine-grit sandpaper to create a smooth surface.
Wipe your chest down with a clean, damp cloth to remove residue.
Using a clean rag, apply wood conditioner to the chest. Wear gloves while doing this. Let the wood conditioner dry for at least 24 hours.
Apply stain to the chest with a clean paintbrush. With a clean rag, wipe off any areas that have excess stain. After the stain dries, sand the freshly stained wood very lightly with ultrafine-grit sandpaper.
Apply another layer of stain several hours after the first, and then do another light sanding with ultrafine-grit sandpaper. Let the stain set until it has completely dried.
Sand the surfaces of your chest with ultrafine-grit sandpaper to remove any uneven staining. Wipe the surfaces down with a clean, damp rag.
Apply a coat of polyurethane sealant using a clean paint brush. Coat the entire surface evenly. Let the sealant dry and apply a second coat. Let the sealant dry for three to five days.