Do I have an egg eater?

I have had 4 chickens for a little over a week now. The first two days I got 3 eggs and then it was 2 and now I am not getting any eggs. They have access to grit, oyster shell and layer feed, I have kept the coop clean, and yet egg production seems to have come to a halt. This afternoon while inspecting for any opening that might allow a snake to sneak in, I came across a small piece of broken egg shell in one of the nesting boxes. I think that I might have an egg eater, which would explain why I have no eggs. I guess I figured that the chickens would make a mess eating the eggs? There has been no sign of shells or yolks left in the coop. Could they be eating the eggs in their entirety and making it look as though no eggs were ever laid?? If this is the case, any suggestion how to find out and how to break the behavior?