Puncture the area surrounding the chewed part of the wooden chair with the point of a scratch awl. Push the awl into the surface approximately 1/4 inch. This will give the wood filler something to adhere to around the damaged area.
Sand the area around the repair with 120-grit sandpaper to scuff the finish, also to allow the filler to adhere to the wood around the damaged part.
Mix the wood filler with the activator, using a putty knife. The activator comes with the filler can in a squeeze tube. Once the activator is mixed into the filler, you will have to work quickly. The filler hardens within 5 to 10 minutes.
Press the filler into the chewed area of the chair. Shape the filler with the putty knife so that it roughly blends in with the rest of the furniture part.
Allow the filler to dry for 15 to 20 minutes. Sand the filler with a progression of 120 to 180-grit paper. Blend the repaired area to match the rest of the furniture part, sanding the filler until the repair is seamless.
Wipe the repaired area down with a tack cloth to clean off any dust.
Brush on a matching wood finish with a poly brush. Allow the finish to dry at least 72 hours before you return the chair to use.