Grilling chicken

The safest answer is no, you shouldn't. Even though you quickly removed the chicken and put it in the fridge, it did not get hot enough to kill dangerous bacteria, nor would it have cooled quickly enough to stop them reproducing to dangerous levels. That all being said, I suppose it comes down to what sort of risk you feel you can take. If the bird was contaminated with salmonella, you could kill it by heating the meat to at least 165F. If that is the only contaminant in the meat, it would then become safe to eat. On the flip side, there are some bacteria out there which produce toxins which are unaffected by heat. So killing them off does nothing to make the food safe. In the end, I suppose it depends on how lucky you feel. I've sacrificed chicken in the past myself- which is why I invested in one of those little stickers for the gas bottle which can tell me how much gas is left inside.