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 chairman of a health trust under fire for not properly investigating the unexpected deaths of patients has resigned.