It is not safe. Not only because it is made out of plastic but because it is 12". At the least the circumference should be 14" and 15" is much preferred. The pole in the center will bend the chinchilla's back as well as the small space. I suggest buying a ChinSpin, Flying Saucer, or a Silver Surfer.
I had one of those wheels when my chin was younger and I was less informed. The plastic is awful, the wheel is VERY loud...
But the worst part is that if a chinnie chews the end of that center spoke, the wheel will fall completely apart. Mine made quick work of it, and there is no way to repair it.