1. Place chicken between 2 sheets of plastic wrap; pound to 1/2-inch thickness using a meat mallet or small heavy skillet. Cut each chicken breast half in half crosswise.
2. Combine curry powder, salt, and 1/4 teaspoon pepper. Sprinkle curry mixture over both sides of chicken. Heat a large nonstick skillet over medium-high heat. Add oil; swirl to coat. Add chicken to pan. Cook 3 minutes on each side or until done. Remove from pan; let stand 5 minutes.
3. While chicken stands, combine yogurt, chutney, green onions, and remaining 1/4 teaspoon pepper in a small bowl.
4. Warm naan according to package directions; cut in half crosswise. Cut chicken into 1/2-inch-thick slices. Spread yogurt mixture evenly over naan halves. Top evenly with greens and chicken; roll up.