The crash happened Tuesday afternoon in the 2900-block of West Addison.
Police said 76-year-old Dolores Sobczak and 96-year-old Johanna Kazak were getting into their car in the parking lot of the strip mall when an 89-year-old man was attempting to park his Chevy Tahoe. While parking, the man had a problem with his gas pedal, police said.
Police said the Tahoe accelerated, striking the two women as well as several parked cars.
Sobczak was killed and her mother was injured.