Mike Petter quit his post ahead of the publication, due on Friday, of a Care Quality Commission (CQC) report on Southern Health NHS Foundation Trust.
He said leaving his post had been a "very difficult decision".
Problems came to light at the trust when 18-year-old Connor Sparrowhawk drowned in a bath at a care facility.
An inquest found neglect contributed his death, at Slade House in Oxford, in 2013.
A report commissioned by NHS England, published in December 2015, discovered that only 272 of the 722 deaths in the trust over the previous four years were investigated.
The trust was issued a warning notice by the CQC following an inspection in January.
In a statement Mr Petter said: "The trust has recently undergone a significant amount of scrutiny in some service areas and, given the challenges it faces, I feel it is appropriate for me to allow new board leadership to take forward the improvements.
"I have been involved in Southern Health since the trust was formed in 2011 as a non-executive director and since August 2015 as chairman.
"It is with great sadness that I now leave the organisation.
"I offer my support and best wishes to all our staff whose dedication and commitment I am continuously impressed by."

The singer-songwriter is one of 85 people from Northern Ireland who have been recognised for their achievements.
The Belfast-born musician, whose full name is George Ivan Morrison, will be known as Sir George. He described his new title as a "huge honour".
Some of the 69-year-old star's biggest hits include Brown Eyed Girl, Moondance and, fittingly, Here Comes the Night.
His knighthood has been granted for "services to the music industry and to tourism in Northern Ireland".
In a statement on Friday, Morrison said: "Throughout my career I have always preferred to let my music speak for me, and it is a huge honour to now have that body of work recognised in this way.
"I would like to take this opportunity to thank all the fans who have supported me on my musical journey."
Morrison was born into a working-class family in east Belfast in 1945 but his exceptional talent has made him a global recording star.
The Rock and Roll Hall of Fame describes him as "one of the greatest singers of all time".
The son of Harland and Wolff shipyard worker, he grew up in a small terraced house in Hyndford Street, in the shadow of the shipyard's famous cranes.
His father's extensive record collection exposed the younger Morrison to a huge range of American musicians, including Hank Williams, Ray Charles, and Muddy Waters.
Those early influences filtered into Morrison's own eclectic style which mixes soul, blues, jazz and country music with pop and rock.
As well as selling millions of records worldwide, he has won six Grammys and a Brit award for Outstanding Contribution to Music.
His relationship with stardom and the media has not always been comfortable. In 1993, he became the first living recipient not to attend his own induction ceremony at the Rock and Roll Hall of Fame.
However, more recently he has accepted other accolades in person, including honorary degrees from both of Northern Ireland's universities.
Last year, he was granted the freedom of his native city and celebrated the honour by playing a free concert at Belfast's Waterfront Hall.
In total, 53 men and 32 women from Northern Ireland have been honoured by the Queen for their achievements in a range of fields and for their contribution to public life.
The second highest honour, Companion of the Bath (CB) was given to the top civil servant at Stormont's Department for Social Development, William Haire, while the chief executive of Belfast Harbour Commissioners, Robert Adair, becomes a Commander of the British Empire (CBE).
Also honoured is one of Northern Ireland leading exponents of the Chinese lion dance, Yuk Shan Lui.
PSNI Assistant chief Constable Will Kerr receives an OBE.
Former East Antrim MP Roy Beggs is awarded an MBE, as is BBC news cameraman Peter Cooper, who recently retired after 40 years.
Other recipients include:
The chairman of a health trust under fire for not properly investigating the unexpected deaths of patients has resigned.
[NEXT_CONCEPT]
Van Morrison has been given a knighthood in the Queen's Birthday Honours list.