Story #6 from The Red Notebook, by Paul Auster.  I took the liberty of slightly abridging the beginning.

R. told me of a certain out-of-the-way book that he had been trying to locate without success, scouring bookstores and catalogues for what was supposed to be a remarkable work that he very much wanted to read, and how, one afternoon as he made his way through the city, he took a shortcut through Grand Central Station, walked up the staircase that leads to Vanderbilt Avenue, and caught sight of a young woman standing by the marble railing with a book in front of her; the same book he had been trying so desperately to track down.

Although he is not someone who normally speaks to strangers, R. was too stunned by the coincidence to remain silent.  “Believe it or not,” he said to the young woman, “I’ve been looking everywhere for that book.”

“It’s wonderful,” the young woman answered.  “I just finished reading it.”

“Do you know where I could find another copy?” R. asked.  “I can’t tell you how much it would mean to me.”

“This one is for you,” the woman answered.

“But it’s yours,” R. said.

“It was mine,” the woman said, “but now I’m finished with it.  I came here today to give it to you.”