Support is highest among people aged between 35 and 44, but falls away among older age groups.
Independent MSP Margo MacDonald is proposing changes to the law in Scotland to make it legal to help someone bring about their own death.
But Mrs MacDonald, who has Parkinson's, said she hoped the poll findings would encourage MSPs, who she knew were privately sympathetic, to "break cover" and back her Bill.
She told a Sunday newspaper: "This poll demonstrates that there is a consistency of people in support of the idea of the individual being able to determine for themselves that life has become intolerable and to seek assistance to bring it to an end."
First Minister Alex Salmond recently said he was "not convinced" by the plans.
But more than 100 Britons have ended their lives at the Dignitas clinic in Switzerland.
Mrs MacDonald added: "The longer the debate goes on and the more proof there is that the right to end your life is supported by a clear majority of voters, the more confident I am that the Bill will become law.
"I know there are a good number of MSPs who agree with me but who haven't yet gone public because they have been affected by the campaign against the bill."
The poll of 1,000 people by Cello MRUK asked whether the law should be changed in Scotland to allow doctors to help people with chronic illness, who want to die, to end their lives.
It found that 68% said yes, 8% said no and 24% said they did not know.
Mrs MacDonald is to lodge her End of Life Choices (Scotland) Bill in the Scottish Parliament next month. So far, it has attracted the support of 21 MSPs.
Assisted suicide is legal in Belgium, the Netherlands, Switzerland and Oregon in the United States.
New guidance was issued in England recently to clarify where prosecutions would be undertaken in such situations - and where it would not be appropriate.
There was no offence of assisted suicide in Scotland and the country's head prosecutor, the Lord Advocate, will not be issuing guidance similar to that south of the Border.
Scots in this situation could find themselves prosecuted under culpable homicide.
The poll for the Sunday Times found support for a change in the law was highest among people aged 35-44, 78% of whom backed MacDonald's proposals.
Among those aged 45-54, 55-64 and 65 and over, support for the Bill stood at 77%, 73% and 63% respectively.
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