The initial idea of Jack Dorsey that resulted in the development of Twitter is available on Flickr. This idea dates back to 2000, when Jack Dorsey signed up to Livejournal. The current wikipedia article on Twitter states that Twitter began as a research project in March 2006 at Odeo, a podcasting company.
The first tweets of some of the oldest Twitter users are still available. The first tweets were published on March 21, 2006, exactly 3 years ago. Happy Birthday Twitter.
Jack Dorsey, 12:50 PM Mar 21st, 2006 - Twitter Message number 20
Biz Stone, 12:51 PM Mar 21st, 2006 - Twitter Message number 21
noah, 1:00 PM Mar 21st, 2006 - Message number 22
Tony Stubblebine, 1:01 PM Mar 21st, 2006 - Message number 25
Evan Williams, 1:02 PM Mar 21st, 2006 - Message number 28
Dom Sagolla, 1:03 PM Mar 21st, 2006 - Message number 31
Tim Roberts, 1:08 PM Mar 21st, 2006 - Message number 36
rayreadyray, 3:40 PM Mar 21st, 2006 - Message number 70
ariel, 4:16 PM Mar 21st, 2006 - Message number 79