Read this short story when I was in high school (almost 20 years ago!)It was called "The 9,000,000 Names of God" or something like that. Researchers visiting mountain monastary, secretly copying these names of God into their laptop (which was science fiction at the time). The last line went something like: The stars in the night sky were going out one by one......

The story is called "The Nine Billion Names of God" and is by Arthur C. Clarke.

The [Dalai] Lama in Tibet has requested the assistance of some scientists to more rapidly calculate the theoretical 9 billion names of God. They have been working on it for three centuries, but anticipate that, using manual techniques, the effort would require another 15,000 years. The computer is to help generate the 9 billion names of God more quickly.

"Well, they believe that when they have listed all His names -- and they reckon that there are about nine billion of them -- God's purpose will be achieved. the human race will have finished what it was created to do, and there won't be any point in carrying on. Indeed, the very idea is something like blasphemy."
"Then what do they expect us to do? Commit suicide?"
"There's no need for that. When the list's completed, God steps in and simply winds things up . . . bingo."
"Oh, I get it. When we finish our job, it will be the end of the world."
Chuck gave a nervous little laugh."

. . .

"Presently George glanced at his watch.
"Should be there in an hour," he called back over his shoulder to Chuck. Then he added, in an afterthought: "Wonder if the computer's finished it's run. It was due about now."
Chuck didn't reply, so George swung round in his saddle. He could just see Chuck's face, a white oval turned toward the sky.
"Look," whispered Chuck, and George lifted his eyes to heaven. (There is always a last time for everything.)
Overhead, without any fuss, the stars were going out."

Thank you so much for your assistance! - I've been thinking about that story a lot lately and now I'll be able to re-read it! I was sure it was Bradbury, but I guess I was wrong.