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:

1. Pour into shallow pans, without lids to maximize surface area & evaporative cooling. Stir every few minutes until it starts to cool down.
2. Place the pot in a sink filled with cold water & ice, and stir every few minutes, possibly changing out the water & ice if necessary
3. 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)

Was it between 140 F and 40 F for more than 4 hours? If so it is in the danger zone.

You also have a possible problem of warming the fridge to over 40 F.

The problem with a large vessel is a larger volume (heat) to surface ratio. This causes it to cool more slowly.

Break the soup down into smaller (like 1-4 quart) covered non-insulated containers before placing in fridge. Need the cover as in the fridge the vapor puts extra load on the condenser and significantly reduce cold produced by the refrigerator.

I would even cool on the counter with a covered to to keep the top surface closer to the temp of the middle.

Let the soup cool towards 140 F before you place it in the fridge to reduce the load you put on the fridge. 140 F is about when you can pick it up with your bare hands. You can let it cool to under 140 F but that is just time in the danger zone. Since the fridge has limited capacity letting if cool to like 120 F if it will do that in less than 30 minutes is probably closer to optimal.

Even in small containers your extra small fridge may not have the capacity to cool the large volume of soup fast enough.

I was brought here from another post flagged as a duplicate that asked about cooling LARGE amounts of soup. I take that as not just one pot of soup. This method will work and cool the liquid to the ambient temperature in minutes. I am a brewer of beer and as such, got tired of cooling my boiled beer (wort) in the sink filled with ice. I just don't have that much ice. So a wort cooler works. It attaches to your sink then a hose goes to a copper coiled tube then water is expelled the other end. You would insert this tube in your liquid and presto I can take liquid from 150 F down to whatever the temperature of my cold water is from the sink. This is standard practice for brewing beer, and would certainly work for any other liquid.