Absolutely throw it away.
Even if you followed 100% the safe cooking guidelines at every step of the process that you had control of the chicken -- you don't know whether somewhere else along that industrial food chain it was contaminated by being left out a little longer than it should have been, or etc.
And, even with 100% safe cooking guidelines, that stock was sitting on the counter at the perfect temperature to grow bacteria for a long time ... you could have a tremendous culture of bacteria in there without knowing it. Those who recommend throwing it out, have a lot of scientific research on their sides -- to reach a temperature high enough to kill the bacteria which likely have grown in your stock, for a long enough duration to kill the bacteria down to a 'load' which is less likely to make your family ill, you'd be looking at a very high temperature for a very long time - which would render your stock pretty much inedible anyway.
I can drive down the highway on the wrong side for miles where I live without seeing another car. Doesn't mean it's safe for me or for my family, and it doesn't mean that there isn't a car coming down the highway that I'll hit, either. Just because people have done this before and not been ill doesn't mean that they WON'T be ill, nor does it mean that it's safe.
The majority of food borne illness is a result of foods eaten at home. "Stomach flu" isn't a random thing - it's pretty much always the result of eating a contaminated food.
It stinks to throw out a food like this - but it would be much worse if you made yourself/kids/guests ill. You can make more stock.
If you really hate to waste it and have a pet - then give it to the pet. But know your pet might get sick, too.
I really like this website for information about food safety, food preservation, etc.:
http://lancaster.unl.edu/food/foodsafety.shtml
(It's by a Family & Consumer Science Educator for the Coopertive Extension Service in Nebraska)
ETA:
If people are leaving stock out on the counter to cool before refrigerating it - here is a
safe method of cooling stock quickly before putting it in the fridge.
We use a Kleen Kanteen for this but I heard of it originally using a plastic pop bottle. Fill the container with water and freeze until it's solid (obviously don't fill to the top or you'll have a burst container).
When you need to cool a pot of soup, broth, stock, or chili -- use the frozen bottle to stir the pot to cool it more rapidly. Once the temperature is cool enough that you're comfortable partitioning it into containers to refrigerate or freeze, then do so. Unless you are making an extraordinarily large pot, you should be able to use one frozen bottle and then refrigerate.
When I learned this technique, I was told that many restaurants use it to quickly cool broths etc. as well. I suspect that there is an actual tool which they use, but our make-do works well too.