The U.S. spelling of the word is theater. It follows our practice of simplifying the British spelling of certain words.
Colour became color.
Manoeuvre became manueuver
Centre became center.
And (you see where I'm going with this, I'm sure) theatre became theater. Whever we write about a place where people put on plays, we're writing about a theater. The owners of the establishment may choose to name it "The World's Best Theatre," and if we use the proper name, we would of course spell it their way.
Once we leave the realm of proper names, though, and enter the inviting fields of generic land, the word becomes theater. That's how our version of the language spells it.