Are private "grand juries" legal?

In another forum the question was raised by a lawyer:

Where is the case law providing that a grand jury can be formed and do anything, other than get indicted, without it being summoned by the clerk of court and empaneled by the court?

There is of course no such case law, although state laws differ concerning the procedures. Some provide for summons and empaneling by different officials, such as the sheriff, or authorize the county government to designate who performs those functions. In Texas state law each county has the authority to use one of two methods of selection: key-man or random.

Everything is ultimately based on some kind of public election. In some states, like Texas, it is possible for citizens to conduct a public election to elect an official who does not otherwise have official authority, to an office that is created by the election. Thus, such a public election could elect someone to a new office such as "grand jury administrator" with the authority to summon and impanel grand jurors not necessarily under the supervision of any particular court, but with the authority to pick their own court for the purposes of enforcing summonses and subpoenas, but the court would not be compelled to enforce them. They could appoint prosecutors by issuing indictments to them, but again, the court does not have to allow the prosecutions in its court.

Enforcement all comes down to custom. The justice system depends on voluntary cooperation among several components and officials, and if they refuse to cooperate, there is generally no recourse but "self-help", which is likely to lead to violence. It should always be kept in mind that courts exist to give people an alternative to violence, to prevent civil disorder. But if all the courts want to close their doors and let the riots proceed, that is their prerogative.