Combine the salsa, peanut butter, coconut milk, lime juice, soy sauce, sugar, and ginger in the crock of a slow cooker; mix well. Place the chicken in the sauce, spoon mixture over chicken to coat.
Place the lid on the cooker and set to LOW. Cook until chicken is very tender and sauce has thickened, 8 to 9 hours. A meat thermometer, inserted into the thickest part of a thigh should read at least 160 degrees F (70 degrees C). Garnish with peanuts and cilantro before serving.