The Kuchisake Onna, or split mouthed woman, is a popular figure in Japanese folklore. She even shows up in many modern day urban legends. She often appears wearing a surgical mask to cover her mouth, which has been ripped open from ear to ear. She will ask unknowing passers-by whether or not they think she is beautiful. Often they will say yes, and she will remove the mask, showing them her torn face and ask again. If the person says no, then she will rip their face so it resembles hers.
There are different rumors about how to avoid her killing you. One is to say she is average, and another is to ask her if you are beautiful, in hopes of confusing her so one could escape while she has to think about what to do next.
The stories of Kuchisake Onna came from the Heian period Japan, where there lived a very beautiful but very vain woman. Her husband thought she was being unfaithful to her, and cut her face out of jealousy.