The founder and CEO’s official account sent a huge number of offensive and irresponsible posts – as well as what appeared to be in-jokes and references to the hackers – over a long period.
The account has more than four million followers, and so is one of the most powerful accounts on the site.
As well as being able to post under Mr Dorsey’s name, and cause embarrassment by revealing the fact Mr Dorsey is unable to keep himself safe on his own app, the hack presumably means that the hackers are able to read his private direct messages.
The hackers referred to themselves as “Chuckle Gang” and directed anyone reading the tweets to a discussion board, though that was taken down more quickly than Twitter was able to remove the posts. The group gave no indication of the motive behind the attack, though it did ask Mr Dorsey to remove the suspensions of a number of accounts.
Whoever was behind the attack also made no reference to how they had actually been able to break into the account.
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Some time after hackers gained control of the account, the tweets were removed. In the wake of the attack, the account appeared to be behaving strangely for some users, with no tweets showing at all.
Neither Mr Dorsey’s account or the official Twitter page made any reference to the hack.
The company said in a statement to media that it was aware of the hack and is investigating what happened.
Twitter encourages all of its users to use two-factor authentication, which is intended to ensure that nobody but an account holder is able to get into an account.
Facebook boss Mark Zuckerberg also had his account hacked in 2016, apparently after declining to use that protection and having an easy-to-guess password.
Jack Dorsey helped to found Twitter in 2006. He initially served as its CEO, before stepping down and then returning to lead the company again in 2015.
Mr Dorsey has been hit by problems using his own site before. In 2016, his account was briefly banned, before being reinstated again.