Mix jalapeño chile, garlic, chili powder, oil, lime juice and salt in 1 1/2-quart slow cooker. Add chicken; coat with oil mixture.
Cover; cook 4 to 5 hours.
Remove chicken from cooker; place on cutting board. Shred chicken, using 2 forks. Return chicken to cooker and mix well. Using slotted spoon to remove chicken mixture from cooker, place 1/3 cup chicken mixture on each tostada shell. Top with lettuce, cheese, salsa and sour cream.