It is almost always a crime to possess a firearm while under the influence of alcohol or any controlled substance. Many states also prohibit people from carrying a firearm into establishments that serve liquor (such as bars and nightclubs), even with a concealed carry permit, and even if you are not drinking.
The laws that apply to you depend on the state in which you live. To learn more about the gun laws in your state, see Gun Control Laws, and click the link to your state under the section entitled "Gun Laws by State".
Having a concealed carry permit does not give you free reign to carry your weapon at any time or under every circumstance that you wish. Most permits come with a set of places or circumstances where you may not carry your gun, and one circumstance is usually while you are under the influence of drugs or alcohol.
This is the case in Tennessee, where as a concealed carry permit holder, you may have your license suspended for up to three years (in addition to fines and possible jail time) for drinking in an establishment that sells liquor while in possession of your firearm.
Penalties for violating firearms laws can include serious fines and long prison terms. If you have specific questions or are facing firearms-related charges, contact an experienced criminal defense attorney.