The skin of the chicken is what gets crispy. So, if you are cooking skinless chicken thighs or breasts, they are not likely to become crispy. Make sure to use bone-in, skin-on chicken thighs if you are looking for crispy skin. To produce crispy chicken in the oven, cook it at 450° Fahrenheit on the top third of the oven, which is the hottest part of the oven. It also helps to occasionally baste the thighs with marinade.