Place the chicken carcass into a large pot and cover with water. Bring to a boil over high heat, then reduce heat to medium-low, and simmer for 5 minutes.
Drain, and rinse the carcass under running water. Return the carcass to the pot along with the galangal, lime leaves, lemon grass, chile peppers, garlic, and shallot.
Pour in 10 cups of water.
Return to a boil over high heat, then reduce heat to medium-low. Simmer uncovered for 1 1/2 hours, skimming the foam and fat often. Strain through cheesecloth before using.
