Along with being a naturally occurring inhibitory neurotransmitter, Gamma-aminobutyric acid is also an over the counter supplement sold to cause relaxation. Although it is somewhat expensive compared to common vitamins, and also somewhat hard to find, it is fairly easy to obtain. In the United States, it is also totally legal, being regulated as a food product, rather than as a drug.
GABA is the basic inhibitory neurotransmitter, and many of the drugs that work on GABA-such as alcohol, benzodiazapenes and barbiturates are fairly heavy substances, legally and pharmacologically speaking. And yet the substance that they are based upon can be acquired easily. And in fact, my unscientific survey of its effects seem to show that it has an effectiveness, as a tranquilizer, somewhere between placebo and a mug of hot cocoa. The best reason for this I have seen cited is the fact that GABA doesn't easily cross the blood/brain barrier: the same reason why a person can't take serotonin as a mood stabilizing chemical. I do admit that the full pharmokinetics are beyond my understanding.
None of this should discourage the person who is seeking a cheap, harmless means of calming anxiety to experiment with GABA. There doesn't seem to be any serious side effects in otherwise healthy individuals, and even though it is comparatively expensive, a month's supply is still cheaper than a single night's supply of alcohol. However, as with all drugs, caution and medical advice is urged.