[p225] OPINION OF THE COURT
ALITO, Circuit Judge:
This is an appeal from a District Court order denying a petition for a writ of habeas corpus filed by Ronald A. Williams. Williams, who is serving a term of life imprisonment in Pennsylvania for first-degree murder, argues that his right to an impartial jury was abridged because the state courts refused in post-trial proceedings to admit certain evidence of racial bias on the part of members of the jury. Williams sought to introduce this evidence to show, among other things, that jurors lied during voir dire when they denied racial prejudice. The state courts refused to consider the evidence at issue based on the well-established evidence rule that generally bars juror testimony for the purpose of impeaching a verdict (the "no impeachment" rule). We hold that the state courts' refusal to receive some but not all of this evidence violated Williams's clearly established constitutional rights, and we therefore vacate the decision of the District Court and remand for an evidentiary hearing at which Williams will have the opportunity to introduce the improperly excluded evidence and to attempt to prove that a juror lied during voir dire.
I.
On August 5, 1984, at about 10:15 p.m., Archie Bradley stepped off a city bus outside a truck depot maintained by his employer, Nor-Sub Trucking, in Cranberry, Pennsylvania. Minutes later, witnesses heard five gunshots nearby. One witness also saw the triggerman standing over Bradley's body and holding a gun. Immediately before the witnesses contacted police, a patrolling traffic officer observed a suspicious car leaving the Nor-Sub parking lot. He noted the license plate and initiated a pursuit that escalated in intensity. The driver of the fleeing car threw various objects out the window, striking the police car with one of them, and succeeded in eluding the officer, but the car overturned on an embankment. Police discovered it abandoned. Retracing the route of the car chase, police recovered a Mac-10 firearm, a silencer, and an ammunition cartridge, and the police matched the gun forensically to the object that had struck the police cruiser. A search of the vehicle yielded more guns and ammunition, as well as a slip of paper on which was written "Nor-Sub 10:15."
In the early-morning hours of August 6, Williams telephoned Jewel Hayes, an intimate acquaintance, explaining that he was stranded somewhere and needed a ride. Hayes agreed, but when she could not find the designated pick-up location, she asked a police officer for directions. Police traced the phone call and arrested Williams and his brother Raymond. The eyewitness to the shooting identified Williams as the gunman. A 911 caller who claimed to have witnessed the vehicle leaving [p226] the crime scene initially described the car as blue and its driver as white, but this witness later decided that the car was gray and the driver was black. The witness eventually identified Williams, who is African American, as the driver. Both parties in their briefs refer to other inculpatory and exculpatory evidence, but none of it has a bearing on this appeal.
During voir dire proceedings in the Williamses' 1985 trial, the trial court asked two questions regarding racial bias:
Do you personally believe that blacks as a group are more likely to commit crimes of a violent nature involving firearms?
Can you listen to and judge the testimony of a black person in the same fashion as the testimony of a white person, giving each its deserved credibility? All the jurors who were selected to serve answered "no" to the first question and "yes" to the second. The jury convicted both Williams and his brother and sentenced them to death.
Shortly after the verdicts were returned, Williams's attorney filed post-trial motions. Among other things, he sought a new trial on the ground that the jury had received and had been influenced by information not introduced in court. In support of this motion, Williams's attorney submitted the affidavit of juror Judith Montgomery. Montgomery, who died in 1996, stated that "prior to the deliberation process as to Ronald Alfred Williams' sentencing," another juror had told the entire jury that, according to information received from an alternate, Ronald Williams had committed two murders, that Raymond Williams was wanted for two other murders, and that, "if this jury did not give the death penalty, (regarding Raymond Williams) another [jury] would." App. 8a.