A few things stand out about this unprepossessing city. It just broke its own Guinness Book world record for the most lighted jack-o'-lanterns with 28,952. It claims to have the world's widest Main Street. And recently, Keene became the home of Justin Somma, a 26-year-old freelance copywriter from Suffern, N.Y., and a foot soldier in an upstart political movement. That movement, the Free State Project, aims to make all of New Hampshire a laboratory for libertarian politics by recruiting libertarian-leaning people from across the country to move to New Hampshire and throw their collective weight around. Leaders of the project...