Chisa Yukizome is a major character in Danganronpa 3: The End of Hope's Peak High School. Technically also overarching protagonist, being the tutor of the Remnants of Despair and ending up as one herself.

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If you're talking to her, you're probably not an Ultimate. Just take it that you encountered her randomly, or something. 

Hope's Peak Academy staff in the franchise are typically very high-maintenance. Yukizome and Munakata seem to be the only sensible ones.