I've discovered my parakeets love to chew corks (and spit out the pieces) The females especially love it when I buy little unpainted birdhouses and fill them with corks. They keep working and chiseling until they empty out the birdhouses.
Now, that sounds like a good idea... human-contact-quality corks, like for wine, etc. I guess they're clean, safe, non-toxic, and as long as they aren't consumed. I like it!