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 website.
Make sure you are familiar with the cancellation policies. Policies vary with each hotel.
Another option to stay is to rent a cabin a few miles from the city. River Canyon Properties has cabins 10 minutes from downtown. They offer one and two bedroom units all fully furnished with balcony views of the river. See links below.