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It is crucial to boil chicken in boiling water, not simmering water. And keep in mind the altitude you are boiling at because it will lower the boiling temperature. We are working with a cooking temperature of 212ºF (100ºC).
Virtually all chicken drumsticks still have a bone in them. So, if you are working with a deboned drumstick, your boiling time will decrease to 10-15 minutes.
On average, a whole chicken under 4 pounds will take about 30-50 minutes to cook completely. A whole chicken above 4 pounds will take between 40-70 minutes to cook.
Frozen chicken thighs will take between 30-45 minutes to boil completely. Chicken breasts (boneless and skinless) will take between 20-30 minutes.
This gooey white stuff consists of mainly water and protein. The proteins denature during the boiling process and leeches out of the meat with water.