I vote for the snake. Always bring in the eggs; a few times a day if possible but keep some gulf balls or wooden eggs in the boxes. You might get lucky and have a snake eat one of those and then it will be much easier to catch/kill. The only thing that can get in my coop is a med to small snake, but there is no way of it getting out if they swallow a wooden egg. It will get jammed.
If it is the chickens, you have a bigger problem and there too, you need to go in the coop often and remove them, because the habbit needs to be broken.
If that is the case, you might need to research some nesting boxes that are slanted and will allow the eggs to roll after being laid, so they will be safely put out of harms way, in a hen proof area. Its more scientific than down home country, but if they develope a taste for the eggs, it is not cool.
Now you also might want to consider if your chickens have enough calcium. Get some crushed oyster shells and spread them around every month or so. I like to give them the shells when we eat crabs or crawfish. They munch on the hard shells and also get a bit of nourishment with what we leave behind; and you should see the egg color the next few days (almost red)....and the taste!! I'm not likely to want to sell eggs a few days after that.
But really.....a clean nest, where you should have had an egg. I think you need to look for a snake's hidding place or make several trips to the coop a day. If your birds are closed in and don't have free-range, you might spread moth balls around. Or better still.....go through your sock drawer and find some ripped knee high stockings and put in a few moth-balls and hang them high in the nesting boxes, out of sight in the dark.