Place each chicken breast half between 2 sheets of heavy-duty plastic wrap; pound to an even thickness (about 1/2-inch), using a meat mallet or small heavy skillet. Combine mayonnaise, soy sauce, juice, and chile paste in a large zip-top plastic bag. Add chicken to bag; seal and marinate in refrigerator 15 minutes. Remove chicken from bag; discard the marinade.
Heat a large nonstick skillet over medium-high heat. Add 1 tablespoon oil to pan; swirl to coat. Place panko in a shallow dish. Dredge chicken evenly in panko. Add half of chicken to pan; saute 4 minutes on each side or until chicken is done. Wipe pan clean with paper towels. Repeat procedure with remaining oil and chicken.