Combine yogurt with olive oil, vinegar, curry powder, and cumin in a large bowl. Add dill, garlic, and lemon zest to the marinade. Season with pepper.
Submerge chicken in the marinade and coat well. Cover the bowl and refrigerate, 2 to 4 hours.
Remove chicken from marinade; let rest until chicken reaches room temperature, about 30 minutes.
Preheat the oven to 375 degrees F (190 degrees C). Lightly grease a baking pan with oil.
Place chicken on the prepared baking pan, making sure chicken pieces are not touching.
Bake in the preheated oven for 15 minutes. Flip and continue cooking until chicken is no longer pink in the center and the juices run clear, 25 to 30 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
Remove chicken from oven and cover loosely with aluminum foil. Let rest for 5 minutes before serving.