Preheat oven to 400°F.
Heat oil in a large cast-iron skillet over medium-high heat. Toss chicken in a medium bowl with ½ teaspoon salt and ¼ teaspoon pepper until coated. Add the chicken to the pan; cook until golden on both sides, 3 to 5 minutes per side. Transfer to a plate. (Do not wipe the pan clean.)
Add butter and lemon slices to the pan. Cook until lemon is golden on both sides, about 1 minute. Transfer the lemon to the plate with the chicken. (Do not wipe the pan clean.)
Add orzo and garlic to the pan. Cook, stirring often, until the garlic is fragrant and the orzo is lightly toasted, 2 to 3 minutes. Add wine; cook, stirring constantly, until mostly absorbed, about 1 minute. Add broth, kale, capers and the remaining ¼ teaspoon salt. Bring to a boil over high heat; stir. Return the chicken, lemon slices and any accumulated juices to the pan.
Transfer to the oven and bake, uncovered, until an instant-read thermometer inserted in the thickest piece of chicken registers 165°F and the orzo is tender, about 10 minutes. Sprinkle with parsley.
