I started cooking chicken soup too late at night. It has boiled for about an hour, but I want to go to sleep and resume cooking it in the morning. Can I leave it on the stove without it developing bacteria?
It's never too late to make a soup! We have often left stock cooking over very low heat overnight, and as long as there was plenty of water in the pot, it has never gotten close to cooking dry.
Your alternative is questionable, though. The soup will develop bacteria as it sits at room temperature overnight. Boiling it the next day when you finish the soup will indeed kill the bacteria, but there are strains of bacteria that create toxins that are not destroyed by boiling.
We've have left stock sitting in the pot overnight and finished it the next day without any trouble, but it does expose you to a greater and possibly harmful degree of risk.
If your stove has a very low setting, you can probably let the stock simmer overnight. If your pot doesn't hold much liquid and you're concerned that it might boil dry, you could set the alarm to check it in the middle of the night however draconian that might seem. The alternative is to put it in the refrigerator for the night and get back to it tomorrow.