The makers of the show are planning to completely re-create Middle Earth for the stage - including Mordor and the Shire!
And they will be searching far and wide, through dale and valley, to find the perfect Frodo because they think he is the most important character.
They reckon it will be unlike any show seen before on a West End stage and will eventually be taken to stages all over the world.
London is famous for its big musicals, like Cats which recently ended after 21 years.
At the moment, the most expensive one showing there is Chitty Chitty Bang Bang which cost £6.5m.
The first two books in Tolkien's trilogy have been massive. They are in the top 10 most successful films of all time.
The third, Return of the King, is due to be released worldwide on 17 December.