I know this thread is old, but if I read old threads, surely others do.
When I was young, me and my sister was sent out every morning to collect rows and rows of eggs, for my grandmother, which lead me to believe they laid early every morning. However after growing up and raising my own chickens I now know this is not the case. I realized no one ever went out to collect eggs any other time during the day. Only 6am every morning. So no telling when they were laid. Mine tend to lay whenever they want. I'll go out early and they'd be a couple in nest that's cool to the touch. I'll go back out around 10 to 11 am and there's more, some cool, some warm last check is around 6 to 7 pm when I'm checking feed, water and making sure their all in for the night and usually will find 1 egg. From everything I've learned about hens, they are on their own schedule. Being an egg drops about an hour or so after she lays to start shaping up for the next lay which is about 26 hours after the last lay means no chicken lays at the exact time everyday.