In a large sauce pan or dutch oven, place the chicken, onion, garlic and Serrano. Add cold water to cover and bring to a boil over high heat. Reduce the heat and simmer until the chicken is opaque and the juices run clear when the thickest part of the meat is pricked with a knife, 15 or 20 minutes for breast, about 30 minutes for a whole chicken. Transfer the chicken to a plate to cool; reserve the broth for another use. When the chicken is cool enough to handle, remove and discard the skin and bones; chop or use your hands to shred the meat as directed in the recipe.