Many hotels are booked ahead of time for the Hooch. The Chattanooga CVB keeps a list of hotels that have availability on their website. See available hotels on the Chattanooga Sports Committee website.
Make sure you are familiar with the cancellation policies. Policies vary with each hotel.
Also, remember to check for local house and apartment rentals such as these:
If you have any questions about hotels in Chattanooga feel free to email firstname.lastname@example.org. Please make any booking inquiries directly with the hotels.