Radiohead have signed up to play a free concert for BBC Radio 2 and will also record a series of interviews ahead of their UK tour.
Radiohead will play the All Points West Festival in Jersey City
Fans can apply for tickets over the phone but other BBC radio networks will also be giving them away on air. Recipients will be chosen randomly.
Radio 2 head of music Jeff Smith said: "You'd be a fool to miss the concert," which takes place in London on 1 April.
Fans can apply for tickets until Thursday by calling 08700 100 200.
The show will be held at the BBC's Radio Theatre, inside its Broadcasting House HQ in central London.
Radiohead recently announced they would not play at Glastonbury this summer because poor public transport to the festival has a negative impact on the environment.
However, they have agreed to headline two out of three nights at the inaugural All Points West Festival in Jersey City, New Jersey, in August.
In October the group released their seventh studio album online and let fans decide what they wanted to pay for it.
In Rainbows reached number one in the UK Top 40 charts in January.