Is there a constitutional right to polygamy?

The ACLU's lawsuit challenging Utah's anti-bigamy statutes are now joined by a prominent libertarian/Federalist Society law professor, Jonathan Turley, who has introduced new lawsuit for the Browns (the polygamous family attempting to overturn Utah's anti-bigamy law).

He writes on his personal blog about how he intends to argue the case before the court:

“We believe that this case represents the strongest factual and legal basis for a challenge to the criminalization of polygamy ever filed in the federal courts. We are not demanding the recognition of polygamous marriage. We are only challenging the right of the state to prosecute people for their private relations and demanding equal treatment with other citizens in living their lives according to their own beliefs. This action seeks to protect one of the defining principles of this country, what Justice Louis Brandeis called ‘the right to be left alone.’ In that sense, it is a challenge designed to benefit not just polygamists but all citizens who wish to live their lives according to their own values – even if those values run counter to those of the majority in the state.