The Royal Shakespeare Company (RSC) production began this morning and continues over the next five weeks.
A cast of six RSC actors are improvising a story, loosely based on Shakespeare's classic romance, over real-time on micro-blogging site Twitter.
The actors have been asked to respond to each other, to the "audience" and to real events as they happen around the world.
Their stream of postings - in 140 characters or less - are being relayed to computers from their mobile phones.
Juliet, played by RSC actress Charlotte Wakefield, is a teenager who finds solace over the fact that she has never had a boyfriend by chatting incessantly on the internet.
In one tweet this morning she linked a YouTube video she had made of her room, pausing on the framed photo of her dead mother Susan Capulet.
On her way to school she tweeted, complete with grammatical errors: "Ok now dads beeping at me from the car!! Gotta dash!! Wish I could tweet at school but... I can't :( I promise I'll be back on after school.
"Jules is over and out!! Xxx"
Juliet's brother Tybalt, who is on the verge of being kicked out of school, has tweeted the likes of: "Gonna be late for class coz i've gotta have breakfast. Couldn't give a crap!"
Tybalt, played by Mark Holgate, also tweeted: "A man can go seventy years without a piece of ass, but he can die in a week without a bowel movement."
.Their sister Jess is training for the London Marathon.
The actors have been asked to improvise around a prepared story "grid" set in modern Britain.
They are writing the tweets themselves, taking inspiration from their character backgrounds and a detailed diary that has been given to them.
Such Tweet Sorrow is a co-production with Mudlark, which produces entertainment on mobile phones, TV and the internet, with funding from 4iP, Channel 4's digital investment fund.