The show focuses on a family who develop superpowers after a plane crash but Chiklis explained that the tone of the series may change.
"Over the course of the next four episodes, it does go decidedly darker," Chiklis told Give Me My Remote. "There's always humour and fun within it, but we wanted to be able to paint on a broader canvas.
"I think it was very smart of [executive producers] Greg [Berlanti] and Jon [Feldman] to start off with some lighter fare and then progress into darker areas. And I'm sure we'll return to the light, but it gives us more leeway to tell stories."
Chiklis also revealed that he enjoys exploring his character Jim as he struggles to come to terms with his powers.
"All of a sudden to be [given] invincibility, you really would - even the best among us - have to fight with the temptation of feeling omnipotent and wanting to effect the change," he said. "And in the case of Jim Powell, he definitely is a good guy and wants to impact a positive change, but that could have negative consequences within the family itself. It's really cool how we're peeling this onion. It's just different."
No Ordinary Family continues on Tuesdays at 8/7c on ABC.