The rind of a cheese is part of the cheese and we highly encourage you to eat it wherever possible! All rinds in the US must be deemed edible by the FDA and so there is no danger in eating them. There are some, however, that do not add to the experience so you don't have to eat them all. 

So, the next time you see a lonely brie rind with all the insides scooped out, give it some love and give it a try!  Because a Rind is a terrible thing to waste.