The rivalry with Chiocciola:
The rivalry between Chiocciola and Tartuca is certainly among the most ancient and deep-rooted, even if there were moments in which the two Contradas had relationships of collaboration and friendship: at a time of serious tensions, an alliance followed from the end of the seventeenth century for about a hundred years. But already in the first decades of the nineteenth century, especially after the accidents that broke out at a Palio in 1814, the situation became difficult again. The misunderstandings were rectified with difficulty, but in the following years the rivalry definitively re-exploded, after the Tartuchin victory of 1910.
From: Wikipedia, l'enciclopedia libera.