The case against a former Ku Klux Klan member accused of murder has gone to the jury after a week-long trial.
Mr Killen was acquitted on related charges in 1967
The judge at the trial in the Mississippi town of Philadelphia said the jury was split 6-6 at the end of the first day of deliberations.
A unanimous verdict is required to secure a conviction.
Defendant Edgar Ray Killen, now 80, denies taking any part in the killings of three young civil rights activists in Mississippi in 1964.
The killings formed the basis for the Hollywood film Mississippi Burning.
In their closing arguments on Monday, lawyers representing Mr Killen called for the acquittal of the former sawmill operator and part-time Baptist minister.
Lawyer James McIntyre said Mr Killen "may have been associated with the Klan" but had nothing to do with the killings and was not present at the scene of the shootings.
"He had a big mouth and he was talking all the time. That's all that he's guilty of," Mr McIntyre said.
The victims became martyrs to the cause of civil rights
However, prosecutors made an impassioned plea for a conviction, saying the victims' families had waited a long 41 years for justice.
"Because the guilt of Edgar Ray Killen is so clear, there is only one question left," prosecutor Mark Duncan said.
"Is a Neshoba County jury going to tell the rest of the world that we are not going to let Edgar Ray Killen get away with murder any more? Not one day more."
The activists were two white men from New York and a local black colleague, who were killed while campaigning for the registration of black voters.
Michael Schwerner, 24, Andy Goodman, 20, and James Chaney, 21, were abducted as they drove out of the Mississippi town. Their bodies were buried at a dam.
Mr Killen, who was a suspect in the original investigation but never convicted, was re-arrested after new evidence emerged.