The United States secured its independence from Britain through the Treaty of Paris in 1783. The second article attempted to define the boundaries of the new nation. This led to further problems and disputes because the borders were often defined vaguely or based on inaccurate maps. For example, it was commonly believed that the Mississippi River extended well into Canada and that there was a "Long Lake" between Lake Superior and the Lake of the Woods.
The treaty established that the border between New Hampshire and Canada would be "the northwesternmost Head of the Connecticut River." That's simple enough until you try to get people to agree on precisely which body of water is that northwesternmost head. It was in this geographic confusion that the short-lived nation of the Indian Stream Republic was born.
Three major streams form the head of the Connecticut River. The government of Lower Canada--that's modern-day Quebec--insisted that either Indian Stream or the Connecticut Lakes constituted the head. New Hampshire maintained that the more northerly Hall Stream was the border. Depending on how these streams were defined, the two nations disputed between 50 to 120 square miles of land.
Wars have started over lesser disputes, but neither the United States or Britain was interested in pressing the issue. The inhabitants, however, were less patient about a resolution of their status. In 1832, 59 of them gathered and wrote a constitution for their area. In it, they proclaimed the establishment of the Indian Stream Republic. You can read much of it here.
The new government ruled over a few hundred settlers. The Indian Stream Republic lasted perhaps as long as eight years until the state government of New Hampshire sent in its militia to enforce its claim. It placed the region under the jurisdiction of Pittsburg, a town just south of the disputed area.
Britain and the United States finally resolved this border dispute in 1842. The Webster-Ashburton Treaty awarded the disputed land to the United States by establishing the border at Hall Stream.
Doan, Daniel. Indian Stream Republic: Settling a New England Frontier, 1785-1842. Hanover, NH: University Press of New England, 1997. Google Books. Web. 13. Nov. 2013.
Heffernan, Nancy Coffey, and Ann Page Stecker. New Hampshire: Crosscurrents In Its Development. Hanover, NH: University Press of New England, 1996. eBook Collection. Web. 13 Nov. 2013.