You should not eat spoiled chicken, even if you boil it. When your chicken goes bad, it will have an unpleasant odor, sticky texture and may have visible mold on the outside of the meat. While boiling chicken does kill some bacteria, it won't kill all of them or the toxins they produce.
Step Away
Raw chicken only stays safe for one to two days if properly refrigerated at below 40 degrees Fahrenheit and one year if frozen at 0 F. Chicken that has been cooked to an internal temperature of 165 F lasts for up to one week in the fridge. If your chicken sits out for one to two hours at temperatures between 40 and 140 F, it will spoil. The problem that spoiled chicken poses is the bacteria that grow and multiply quickly within it, which can cause foodborne illness.
The Tough Bacteria
Some dangerous bacteria like Escherichia coli -- nicknamed E. coli -- and Salmonella are killed by heating or boiling it until the internal temperature reaches 165 F. Others, like Staphylococcus aureus, produce toxins that are unaffected by heat. Clostridium bacteria can produce a heat-resistant spore that still leaves the chicken contaminated. These microorganisms make eating spoiled chicken, even if boiled, dangerous, and will also make it taste bad. Throw away any meat that you're unsure of or that has been out on the counter too long.