Noel Conway, 67, who suffers with a form of motor neurone disease, was granted a judicial review earlier this year.
The hearing started this morning at the Royal Courts of Justice in London, with Mr Conway arguing that terminally ill, mentally competent adults should have the right to request an assisted death.
The hearing, which is scheduled to last until Thursday, will see Mr Conway's legal team ask the courts to declare that the blanket ban on assisted dying under the Suicide Act 1961 is contrary to his rights under the Human Rights Act.
More than 200 people turned out to show their support for Mr Conway at a special event held on a boat in Westminster on Friday.
Speaking afterwards Mr Conway said: "I want to thank everyone who has demonstrated today for this wonderful support. In the past months I have been struck by the number of people who, like me, want the right to choose how we die. Today has shown the huge strength of feeling of people who want the right to a dignified death.”
Sarah Wootton, chief executive of Dignity in Dying, said the court would consider detailed evidence on whether the law breaches Mr Conway's human rights.
She said: "The British public overwhelmingly support a change in the law to give terminally ill, mentally competent adults like Noel the choice of an assisted death. The huge turnout for Noel and his family today is yet another demonstration of that support.
"Noel, supported by Dignity in Dying and his legal team, has had to fight hard to get his case heard. We are indebted to Noel and his family for devoting so much time and energy to this case and we look forward to next week’s High Court hearing which will consider detailed evidence and legal arguments about whether the current law breaches Noel’s human rights."