When I babysit my sister's chow, she has an absolute rule for me - that is to NEVER feed a Greenie to her dog. Her dog Beatrice has had nothing but trouble with them (puking). When Beatrice first had one and puked, my sis did a lot of research on them and came up with lots of info indicating they were not a healthy treat, but I know you have to take everything on the Internet with a grain of salt. All we can say is that they don't agree with Beatrice.
There is a version of Greenies for cats too. My cats first took to them and they were definitely kitty crack for them. I used to keep a few in the pocket of my jeans and pull one out as a treat every now and then… until... my jeans went into the wash with them, and even with warm water, soap and lots of rinsing they did not even decompose at all. That was the last time I fed my cats Greenies.