Given that the chicken is not contaminated by poison, and it simply dies of heart failure or heat stroke and not anything that makes it immediately inedible, how long does it take before a dead chicken becomes inedible?
I will post as an answer as too long for comment, but would support closing as opinion based with no definitive answer.
When I raise meat chickens, my answer was zero. Even if the cause was harmless, the meat would be low quality at best due to lack of ability to remove blood. Even simple heart failure, besides the lack of ability to purge blood, could result in contamination from systemic issues related to poor circulation. Note that consumption of down birds was blamed for spreading Avian Influenza in Asia. The use of down animals was responsible for a widespread Mad Cow recall in US and Canada a few years ago.
At times, and in many cultures, using down animals, either dead or dying, has ranged from acceptable to taboo. I personally side with the taboo argument. I hate to waste an animal, but the risks are too high for me.
If you just go with raw guidelines then 2 hours.
By not dressing (gutting) I don't think there is basis to extend that. But I know a lot of hunters including myself that go 4+ hours before dressing a bird and getting it on ice.
Not my intent to imply two hours is good with "If you go with guidelines then 2 hours". I just don't know. If you find guidelines they are not going to assume the bird died of natural causes. See answer from dlb.
If you just search on road kill a common guideline is clear eyes but that is something I cannot find any actual testing data on.