Boiling or poaching chicken means cooking it in hot liquid. This is an ideal quick method for cooking chicken breasts, which can dry out when roasted or grilled. Bone-in breasts with the skin on are a good choice if you want the cooking liquid to become a tasty broth. For a shorter cooking time, opt for skinless, boneless chicken breast halves. For the quickest cooking time, use cut-up or cubed chicken breast.