Hanks and Wilson are both named as defendants in the lawsuit, along with Chet.
In court documents obtained by PEOPLE, the plaintiff, Terry Moogan, accuses Chet of driving while "under the influence of drugs and/or alcohol" when the alleged car accident occurred in Los Angeles.
Moogan asserts that because Hanks and Wilson were aware of Chet's state and are owners of the vehicle, they should be held partially responsible.
"Despite knowing that Chester Hanks was a careless and reckless driver and a habitual user of drugs and alcohol, they negligently permitted Chester Hanks to operate their vehicle, and thus, in addition to Chester Hanks, are responsible for the physical and emotional injuries Mr. Moogan sustained," claims the suit.
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Chet, 25, came clean about his struggles with addiction earlier this year, admitting that he went to rehab over the summer.
Since opening up about his past drug problems, the aspiring rapper has been keeping a low profile and focusing on having a new positive outlook on life.