They are contributing to the libretto line by line, their imaginations limited only by the format of the micro-blogging site, which allows a maximum of 140 characters to be posted at a time.
The results will be put to music and, if all goes to plan, performed to an audience next month.
Royal Opera House spokeswoman Alison Duthie said the use of Twitter is part of a wider effort to get more people interested in the art form.
"It's the people's opera, and the perfect way for everyone to become involved with the inventiveness of opera as the ultimate form of storytelling," she said.
She encouraged people to contribute to the libretto and to view the work-in-progress at http://twitter.com/youropera.
What's taking shape is strange even by opera standards. So far, the libretto tells the story of a man kidnapped by birds and features a talking cat.
Get Action News on your website
