Place chicken in the bottom of a slow cooker. Sprinkle with chili powder, garlic powder, cumin, and onion powder. Top evenly with salsa and green chile peppers.
Cook on Low until chicken breasts are very tender, 6 to 8 hours. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Shred chicken with 2 forks.