1. Preheat oven to 500°. Meanwhile, place chicken thighs, skin side up, on a cutting board. Place plastic wrap over chicken; pound chicken to about 3/4-inch thickness using a meat mallet or small heavy skillet. Pat chicken skin dry with a paper towel. Sprinkle chicken evenly with salt, paprika, and pepper.
2. Heat a 12-inch cast-iron skillet over medium-high heat. Add oil to pan; swirl to coat. Add chicken to pan, skin side down; cook 8 minutes (let them be until the edges start to turn golden). Transfer hot pan to oven. Bake at 500° for 7 minutes. Turn chicken thighs over, and bake an additional 4 minutes or until chicken is done.