It is safe to eat cooked chicken left out for 4 hours.
While the health department has to regulate food establishments on when to throw out food and how long to leave out the food it does not mean that the food actually spoils or has bacteria after that time period.
Although it's not recommended to eat cooked chicken that is left out longer than 2 hours as it could potentially make you sick, it generally is okay to eat the cooked chicken that was left out longer than a couple of hours.
I've personally have eaten cooked chicken that was left out for 4 hours and even overnight before and never gotten sick from it.
Bacteria can grow rapidly on food left out at room temperature for more than 2 hours.
If food is left out in a room or outdoors where the temperature is 90 degrees F or hotter, food should be refrigerated or discarded within just 1 hour.
I don't make it a habit of eating cooked chicken or other meats or foods left out too long but when I've done so I was okay.
As long as the meat or cooked chicken still smells good or has no mold etc on it then it's generally safe to eat.
You could reheat it and kill off some bacteria that could be on the chicken.
The health department is not always right but they have to be so strict to prevent people from becoming sick and suing the food establishments and possibly leading to someone's death.
But at home it's just up to you and if it looks okay then it's usually okay to eat.
However if not eating the cooked chicken within an hour or so you should refrigerate it and it will keep for around 7 days.