removing smelly cigarette smoke

I recently recieved an entire dresser set including a vanity from my boss's mom. She must've smoked all her cigarettes in her bedroom with the door and windows closed every night since she bought the set in the 40's. Now the dressers have this awfully overwhelming smell to them. I'm on the verge of getting rid of the set, but it's a nice one and I'd rather not. It turns my clothes very smelly. Does anyone know of how I can rid these dressers of the smell once and for all?

Thanks,
Sofie