Abraham Lincoln would disagree.
Texas was part of the confederacy during the American Civil War and wasn't spared or allowed to secede.
Gov. Rick Perry have announced that the state of Texas has no such aspirations and will remain within the Union.
Perry spokesperson Catherine Frazier tells CBS News that the governor “shares the frustrations many Americans have with our federal government,” but “believes in the greatness of our Union and nothing should be done to change it.”
As to the lawfulness side of the matter, it depends on the person interpreting the law, if it's Prof. Eugene Volokh from the UCLA scool of law, then he would say:
But at the same time, surely this must be a judgment based on how we see the world today, not based on what happened 144 years ago. A matter is “settled” by political decision only so long as the political decision commands the adherence of the polity. If in 2065 Alaska, California, Hawaii, or Texas (just to consider some examples) assert a right to secede, the argument that “in 1865, the victorious Union government concluded that no state has a right to secede in opposition to the wishes of the Union, so therefore you lack such a right” will have precisely the weight that the Americans of 2065 will choose to give it — which should be very little.
And beyond that, even if there is some precedent of some sort properly set by the Civil War (and I continue to disagree that there is), any such precedent can’t tell us much about consensual secession. The talk I occasionally hear of secession (again, talk that I think is not really serious) is not about departure in the face of military opposition — it’s about creating a political sentiment in some place in favor of seceding, and a political sentiment in the rest of the country in favor of allowing the secession. The results of a bloody civil war tell us nothing about the propriety of a Velvet Divorce.
But that’s not a “settlement” of the secession question for the centuries. And there can be and should be no such settlement. “The past is a foreign country: they do things differently there.” So the present is different from the past, and the future from the present. Poetic allusions to a peace treaty resolving one particular conflict can’t tell us what is right to do in our country today.
However, Justice Scalia says that (Thanks to Oliver_C for the link):
... principally because I cannot imagine that such a question could ever reach the Supreme Court. To begin with, the answer is clear. If there was any constitutional issue resolved by the Civil War, it is that there is no right to secede. (Hence, in the Pledge of Allegiance, “one Nation, indivisible.”) Secondly, I find it difficult to envision who the parties to this lawsuit might be. Is the State suing the United States for a declaratory judgment? But the United States cannot be sued without its consent, and it has not consented to this sort of suit.
(Emphasis is mine)
So it really depends on your interpretation of the law, I however, not being a US citizen or resident, tend to agree with prof. Volokh, because if in the future there will be a situation where a state or a territory will want Independence, and the rest of the USA will be willing to give it to them, then the secession will be preformed peacefully, if the USA will not be willing to grant it, then there probably be some sort of bloodshed.