It's not the amount of rawhide that's dangerous. In fact, according to North Central Animal Hospital, it's rawhide itself that can be a problem, even if you only give your dog a very small piece.
The first problem with rawhide is that there are no FDA regulations regarding its production. That's because rawhide is not considered pet food -- it's a byproduct -- so there's no control over what ingredients are used in its production. North Central Animal Hospital points out that mercury, pesticides and other dangerous chemicals have been found on rawhide.
Aside from the chemical dangers associated with rawhide, there's one more potential risk. According to WebMD Pets, if your dog swallows a large piece of rawhide, this can result in a blockage as the piece becomes logged in the throat or intestines. This could lead to choking or it could require surgery. Small pieces can get stuck in the guts as well.