Yes
I voted yes. Here's why:
Most chinchillas (and most other animals) won't swallow enough plastic to actually cause blockages in their digestive system. All of our pens, shelves house, etc are wood and each pen has toys and other chewing objects, but we have found that some chins still will nibble on plastic where they find it. So if they don't eat enough to cause blockages, why is it bad?
Well, in 1998 DINP (di-isononyl phthalate), a chemical used to soften plastics began to be removed in children's toys from many countries, because lab animals that had been chewing on plastic containing it sustained liver and kidney damage as a long term effect and had significantly higher cancer rates. The U.S. CPSC stated "Animal studies show that DINP causes chronic toxic effects to the liver and other organs...the maganitude of the risk is directly related to the amuont of DINP released from mouthing and the amount of time children mouth the products." Unfortunately, the ban on the use of DINP did not extend to animal products. DINP is not found in all plastics, just soft plastics.
What about hard plastics? Center for the Evaluation of Risks to Human Reproduction (CERHR) has done extensive studies on Bisphenol A, found in hard plastics, that the government has thus far ignored. Their conclusive findings are that the long-term effects of ingestion of Bisphenol A significantly damages the reproduction system, and they have been trying to ban the substance for years.
So, to be on the safe side, we do not allow our chins the oppotunity to chew on plastic. But it is an individual choice. I just believe it is important to make a thoroughly informed decision.