The Donmar Warehouse is opening its year-long West End residency at the Wyndham's Theatre with its production of Chekov's Ivanov.
Kenneth Branagh stars in the play, which is directed by Donmar artistic director Michael Grandage.
It is hoped the residency will encourage more people to watch straight plays in the West End.
Grandage told the BBC he wanted to "address" the dominance of musicals in the heart of London's theatreland.
Ticket prices are also being kept low for that reason, with the best seats priced at £32.50.
Grandage said: "If we don't make the theatre accessible through pricing and through the kind of programming we do then nobody will come and then it will all dry up and I think there is a place for that in the West End.
"Right now there is a debate going on about whether the straight play is still valid in the West End, the fact that musicals seem to be taking over.
"I think we want to address that with the Wyndham season."
The Donmar will continue to put on productions at its Covent Garden venue at the same time as it occupies the nearby Wyndham's Theatre.
Branagh plays Ivanov - a Russian landowner who has lost his appetite for life and is battling money and marital problems.
The theatre must fill 80% of its 750 seats for the production to break even.
Ivanov has been adapted for the production by Sir Tom Stoppard, who acknowledged Branagh's presence would help draw in the crowds.
"It is hard for a straight play to survive in the West End if it does not have any actors in it that the public recognise in some way," he said.
"My view of the matter is very simple: I think Kenneth is a great actor. I'm not going to hold it against him that he's a star."