"I'm not complaining about it, you know, it is what it is and it's cool," he said at LAX on Friday. "I love my dad, he's a great man, he's a great actor, so I'm in a good position, you know what I mean?"
But he added: "If I invented a cure for cancer tomorrow, in the article it would say, 'Tom Hanks' Son Invents The Cure For Cancer,' you know what I mean? It's inevitable."
The 29-year-old, who is the Oscar-winner's eldest with wife of 31 years Rita Wilson, insisted you have to "work twice as hard because everyone's gonna think that everything was handed to you."
"And that's not the case. Everything I've got I had to earn myself, I had to go and audition for every role I got, just like anybody else." he said. "It's not like I'm just gonna make a phone call and — boom — you're in it; that's not how it works."
Chet has etched out a successful career on the small screen with recurring roles in "Empire", "Shameless", "Maron" and "Curb Your Enthusiasm".
He also had small roles on the big screen in "Fantastic Four", "Project X", "Indiana Jones and the Kingdom of the Crystal Skull", and opposite his dad in "Larry Crowne".
While Chet knows his father has the ability to pick up the phone and land him a role in pretty much anything, he knows that serves neither of them.
"He could do that, but he's not gonna do that," he said. "And even if he did do that, it'd be an L for me because if I wasn't ready to earn that role myself I'd be walking into a situation I wasn't prepared for."
Chet, who previously struggled with cocaine addiction and entered rehab in 2015, is currently filming a project with Bryan Cranston in New Orleans, and is equally focused on his music career — a cross between country and rap — with his group Something Out West.
Tom Hanks has two older children from his first nine-year marriage to Samantha Lewes — Colin, 41, and Elizabeth, 37. He also shares 23-year-old son Truman Hanks with Wilson.