He was convicted in the murder after their bodies were found in the family's SUV just off I-55 in Channahon.
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However, lawyers for Vaughn claim investigators manipulated DNA test results, which they say helped lead to the original indictment.
RELATED: Attorneys for Christopher Vaughn, Oswego man convicted of murdering wife, 3 kids, seek his release
Vaughn's parents are asking for a new trial.
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The Will County State's Attorney provided a statement Wednesday saying:
"In the successful prosecution of Christopher Vaughn, we called 90 witnesses to the stand in our case-in-chief and the jury returned a guilty verdict in 60 minutes."
Vaughn previously claimed his wife killed their children before killing herself.