One of the great things about riding a bike is that you can typically lock your bike right in front of your destination without having to circle the block looking for an open parking space. Here is a Google map of bike racks in Chattanooga. There is also a Chattanooga Bike Parking Locator that uses your location to show the closest bike racks to you. If you would like to help contribute bike parking information, you can do so on the GitHub site.
If a bike rack is not available near your destination, you can lock to a parking meter. To learn proper bike locking technique, check out these tips from the San Francisco Bicycle Coalition.