By the way if you want to get more replies from like experts than you can post this same question here: https://www.backyardchickens.com/f/18/chicken-behaviors-and-egglaying
That is very strange, are you sure she layed the egg that was broken i mean some other chicken could have gone in the nest and layed an egg and then the 3 1/2 month old chicken accidently broke the egg when she went in the nest. I am no expert so i am not sure if you should be concerned or not...