Obviously all new employers will perform pre employment checks.One should be forthright in informing new employer about what happened and what actions you took in trying for smooth exit.
I do hope your problems which made you exit are solved and now things are smooth path for continuing further employment.
Highlight this aspect and suitability for employment.
I am sure you have met all targets during 3 year employment with MNC.
They must have graded you in their yearly assessments.
I am sure they also would speak of your general ability to be productive team member.
It becomes a battle to convince new employer,but you have no choice but to face it strategically and intelligently.
3rd April 2015 From India, Pune