Hot chicken soup takes hours to cool
There are people that are going to argue that yes, you do.  And if you're immune compromised, that's probably best.

However, if it had been boiling, and there's a layer of fat to seal the top, then it's at a lower (although not non-existant) risk.  You have to judge for yourself if it's worth it.

Personally, I'd bring it back up to a boil for 30+ minutes, then use other techniques to cool it back down:


Pour into shallow pans, without lids to maximize surface area &amp; evaporative cooling.  Stir every few minutes until it starts to cool down.
Place the pot in a sink filled with cold water &amp; ice, and stir every few minutes, possibly changing out the water &amp; ice if necessary
Put ice, freezer pack or similar into a ziplock bag, put it into the pot, and stir


If you're ever in the situation where it's getting late, and you have a large pot to go into the fridge, I'll either leave it on warm overnight.  (making sure there's nothing near the stove that might be dangerous.  But I have an electric stove, not gas), or I'd do what cooling I can (pot in sink ice bath + stirring), move it into multiple smaller containers, and put them in the fridge without lids on them (so we have some evaportative cooling in the fridge)