I had this problem for awhile too. I have Buff Orpingtons who were the culprits, but they were pecking at the eggs to eat them. It happened before they started laying their own eggs. We watched them carefully and saw it was mainly a certain one. We were all set to cull her when we tried an idea from on here, we put golf balls in the nests and started collecting really frequently and put a curtain up so that she didn't see the eggs.
She was pecking at them and would sometimes peck them open and consume the whole thing, leaving nothing.
The golf balls cured her however, since they are always there she probably gets nothing most of the time and the chickens sure seem to think they are eggs, they always like to lay their eggs where the golf balls are.
The golf balls were also free, they were old used ones from my mom, who golfs.
I would not leave the eggs in there so long, I'd collect them as frequently as possible if I were you. That seemed to help our problem here.