Place the chicken carcasses into a large (8 quart) slow cooker.
Place the Hatch chiles, onion, carrots, bay leaf and thyme into the slow cooker, tucking ingredients around and on top of carcasses.
Pour the water over the ingredients, adding more if needed to bring the level to the top of the slow cooker.
Set the slow cooker to low, and the timer to 24 hours.
When stock is done, strain the stock into a large bowl or pot through a double layer of cheesecloth.
Place the bowl into an ice bath to cool the stock quickly, then refrigerate until completely cool.
Remove and discard any fat that has solidified on the surface. Keep refrigerated until ready to use.
Use or freeze stock within 2-3 days.