Constitutionally is it possible? Yes. There is nothing in the Constitution that I know of that makes or claims to make leaving the Union illegal or even difficult.
In practice, eleven states did leave the Union at one point, the crescendo a serious argument (one that had been raging for 80 + years) that got quite heated. Four years and 620,000 dead soldiers later, the answer was no.
In practical terms, today: to state it bluntly in what I think is correct British English: Not bloody likely. The States are so interwoven with the Fed. gov't that I cannot see how they can separate. By that I mean actual separation, not instituting local laws, customs and so forth. Some states are large enough to do so, both in area as well as in population and economic terms; California has 40 million people and the sixth largest economy in the world, ranking right behind the UK in fact. With a coastline and both large cities and very rural areas, it <could> be a country as far as I can see. There are more than a few, both inside as well as outside California, who would like to see it become a country. :-) But I cannot imagine a path that would lead to Californian independence and in the end, I do not believe it would be beneficial, overall, to either the Country or that State to be independent.
All of that said, our system of States united to form a country is an odd one and has significant results. Very serious things may be limited or outright illegal in one state are perfectly legal and common in another state. We are now seeing more and more stages or steps in differing behavior, and a relatively new thing which is States passing laws making certain Federal behavior 'illegal' in those states, the most important, at least in my view, are the laws preventing the seizure of property w/out due process. An interesting and to my knowledge, untried concept and one that is essentially backwards; Federal laws and gov't override and triumph over State level gov't normally. So it remains to be seen just where the lines will end up, if they even settle at all, regarding State to Federal relationship(s).
Brian
random morning thought/
Constitutionally is it theoretically possible for one of the 50 States to "leave" the USA and declare independence if a mandate of that States population were for it?
Ie a Stexit (State exit)