I forgot the chicken out on the counter-top all night. How do I dispose of it?
You dispose of it like you would with any other meat-based remains that are unfit for human consumption. 

Depending on your local trash system that may mean anything from throwing it out of the window to wrapping it up and putting it in a specific trash or recycling container. Your local waste management company or municipal office can give you better advice than we can.

What I wouldn't recommend though is throwing it on your compost heap - it might invite various animal life forms that you do not want near your house and the smell is quite pungent after a while.