Songfacts®:

• Brian Eno told the London Times how he and Byrne got together for their first album since 1981's seminal My Life in the Bush of Ghosts. He said: "I bumped into David in New York. We had dinner together and I happened to say I had a lot of music I had intended to turn into songs, but hadn't got round to. He said: 'Oh, I've got a few lyrics.' It was as simple as that."
• This was the first fruit from their collaboration after Eno had sent Byrne some instrumental tracks on a CD. Byrne wrote on his website the story of this song: "I attacked the first one, which I think was called 'And Suddenly' on Brian's track list. I'd just finished reading Dave Eggers book What is the What?, about Valentine and his hallucinatory and horrific journey as a very young man that took him from his destroyed village in Darfur to Atlanta Georgia and beyond. Valentine's story was harrowing but also beautiful, uplifting (in a non corny way) and at times even funny. I think I might have still been under the influence of his story when I sat down in front of my microphone. The result became 'One Fine Day.' I sang a few harmonies in the choruses to make it sound better and send it off to Brian. We were both thrilled- here was the gospel-folk-electronic aspect I at least had heard hints of had come to life- articulated. The words had some Biblical allusions, but nothing too overt. We agreed to continue, for now."
• Eno revealed to Rolling Stone magazine that Coldplay's Chris Martin came close to collaborating with him on this rather than Byrne. Eno explained that he played a piece of instrumental music in his London studio for Martin: "Chris said, 'Wow, I'd love to work on that.' I'd given it to David a few months before and hadn't heard anything back. So I gave it to Chris."
  Six months later, on the same day that Martin told Eno he had written "the most amazing song" for that track, Byrne finally e-mailed him an MP3 of this song. The Art Rock legend told Rolling Stone that Martin responded by saying "I can't do better than that." Eno added with a chuckle, "Incredible timing."