Chattanooga was not there.

The name of Indian Maiden's Cliff--applied to a precipice that hangs
above the wild ravine of Stony Clove, in the Catskills--commemorates the
sequel to an elopement from her tribe of an Indian girl and her lover.
The parents and relatives had opposed the match with that fatal fatuity
that appears to be characteristic of story-book Indians, and as soon as
word of her flight came to the village they set off in chase. While
hurrying through the tangled wood the young couple were separated and the
girl found herself on the edge of the cliff. Farther advance was
impossible. Her pursuers were close behind. She must yield or die. She
chose not to yield, and, with a despairing cry, flung herself into the
shadows.

Similar to this is the tale of Lover's Leap in the dells of the Sioux,
among the Black Hills of South Dakota.

At New Milford, Connecticut, they show you Falls Mountain, with the cairn
erected by his tribe in 1735 to chief Waramaug, who wished to be buried
there, so that, when he was cold and lonely in the other life, he could
return to his body and muse on the lovely landscape that he so enjoyed.
The will-o'-the-wisp flickered on the mountain's edge at night, and
flecks of dew-vapor that floated from the wood by day were sometimes
thought to be the spirit of the chief. He had a daughter, Lillinonah,
whose story is related to Lover's Leap, on the riverward side of the
mountain. She had led to the camp a white man, who had been wandering
beside the Housatonic, ill and weak, vainly seeking a way out of the
wilderness, and, in spite of the dark looks that were cast at him and
her, she succeeded in making him, for that summer, a member of the tribe.
As the man grew strong with her care he grew happy and he fell in love.