Cut chicken into bite-size pieces and stir into yogurt until completely covered. Cover and marinate in refrigerator for at least one hour.
For yogurt sauce: Combine yogurt, cucumber, onion, black pepper, salt and red chili powder. Stir until smooth. Refrigerate until ready to serve.
Heat oil in skillet over medium-high heat.
Add chicken and all the marinade to skillet and cook for about 20 minutes or until chicken is cooked through. You may need to drain some liquid from the skillet while this cooks as you want to end up with only enough sauce to coat the chicken.
To serve: You may cool the chicken pieces slightly before serving or keep them hot. You may warm the tortillas, if desired, too. Roll up the wrap with the chicken, yogurt sauce, lettuce or spinach leaves, chutney, rice, tomatoes, radishes and whatever else you like.