Jeffrey MacDonald, the Green Beret doctor, convicted of killing his wife and two daughters in the 1970s, could get a new trial. A federal judge began hearing testimony Monday morning.

MacDonald says a group of hippies broke into his home in 1970 and killed his wife and two daughters. He also says they chanted “kill the pigs” and “acid’s groovy” before they stabbed him in the lung.

MacDonald and his attorneys will attempt to use DNA testing to show that hair samples under one of the victim’s fingernails did not come from him or a member of his family, but from one of the killers.

MacDonald was convicted in 1979 and is currently serving three life sentences for the murders.

Watch the video above to see In Session’s Jean Casarez and Christi Paul talk about MacDonald’s chances of getting a new trial.