Tennessee might technically be able to nip you twice for online gambling, not that either of them is actually going to happen. First, any form of gambling not specifically authorized by the state is illegal, second, using any implement for the purposes of gambling causes it to become an illegal gambling device. The latter part would almost certainly apply to computers. The act of gambling, as a player, is a Class C Misdemeanor.

As we found on our restrictions page, which has a number of interesting Tennessee gambling laws:
The penalty for the mere act of gambling is a fine of not more than $50 and imprisonment for up to thirty days.
We have found a few examples of illegal poker rings and an illegal lottery that had been busted up in the state, but all of these activities focused on operators as opposed to mere players. Some people who were acting just as players may have been caught up in one of the poker stings, though.
Despite Exhaustive Searching
We could find no incident of someone being arrested for gambling online in the context of just being a player, though we are sure they would be all over anyone operating an online casino from within the state. Since any possible penalties on players do not seem to be enforced, the majority of online casinos that accept players from the United States, if not all of them, accept players from Tennessee.
You can search for online casinos that offer you their services below: