The theater was so small, it was named the Little Theater. That was 106 years ago, and since then it has been reincarnated many times — renamed, repurposed, rehabilitated.

Now known as the Helen Hayes Theater, the smallest house on Broadway is about to reopen yet again, this time run by a nonprofit, becoming the sixth of today’s 41 Broadway theaters to operate outside the commercial marketplace.

The 589-seat playhouse has a new mission: Second Stage Theater, the nonprofit group that now owns the structure, says it will be used to present work by living American playwrights, a form of counterprogramming at a time when Broadway is dominated by musicals, revivals and British imports.