poo covered egg

Hello, I have three chickens and for a week now one of them is laying an egg with a lot of poo on the shell.  The nesting box is cleaned out daily as is the floor of the coop - so there is not poo left lying about, however they do tend to lay beofre I clean out the coop.  Why is this happening- and why does it only affect the one.  What can I do to stop it as by the time I collect the eggs at 9.30 the poo has already caked on and is v.difficult to remove.  All hens are in very good health and free range all day.  Thanks.

mine tend to poo in the nest box overnight so when I wake them up I poo pick the nest box, which only takes a second (I only have one  )

If they get poo on the eggs you can just brush it off with some clean straw or a rub with the dry bedding (Aubiose or whatever) failing that your hand will usually do the job 

Have you checked her vent?  Not sure if this is possible but maybe she has poo around her vent and that is transferring to the egg when she lays it?  Just a guess though, not based on experience or fact!

I rarely get clean eggs these days ...

I put some dry Aubiose or hemcore down. Straw would do just as well