Police are investigating a car crash that killed a pedestrian ... which may have been partially captured on a TikTok live stream, TMZ has learned ... the incident went down November 3 in Zion, Illinois, a suburb north of Chicago.

Zion PD tells TMZ ... officers responded to a local intersection for a crash involving a 2015 Ford Edge and a pedestrian identified as 59-year-old Darren Lucas . According to police, the driver -- an unidentified 43-year-old woman -- called 911 and remained at the scene, speaking with investigators.

Lucas was transported to Vista East Medical Center, where he was pronounced dead, police tell us.

Later, Zion PD was directed toward a live stream from TikTok user Tea_Tyme_3, which appeared to capture the driver addressing the camera while at the wheel. In the vi

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