It comes from a Cherokee story of a maiden who fell in love with a man from another tribe. Her parents tried to dissuade her from the romance so she took it upon herself to journey across the ridges to her man. She being a chubby young woman, the mountain was named for her. The English equivalent became "Chunky Gal Mountain".
Thank you, Bob. I, too, read a story similar to this but still find it difficult to find documented agreement on the story. Still, yours sounds like a probably tail. I've updated the image caption to reflect this and encourage others to read your story!