Is it okay to leave uncooked chicken over night but refrigerate it in the morning and then cook it?
We don't refrigerate food because it needs to be cold at the moment of preparation, we refrigerate it because it keeps the "bad stuff" from growing in the first place. Something that's been at room temperature overnight has had plenty of time to grow harmful bacteria, and putting it in the fridge won't change that. It may slow the growth of further bacteria, but you're already in the "do not eat" zone, so you'll only be chilling bacteria-ridden, inedible meat.

While boiling will kill the bacteria that has grown, it may not eliminate nonliving toxins that those bacteria produced while they were alive. Even if you boil it, the chicken is not safe to eat.