It's a playful, somewhat nonsensical way of expressing that they don't want cheese or that something is not cheesy.
The origin of the phrase isn't explicitly stated in the show, but it's likely just a random, made-up phrase created by the characters to be funny and add to their unique slang.
Here's how it's often used in the show:
* Carly: "I'm not in the mood for pizza. No chiz!"
* Sam: "That new boy band is so cheesy! No chiz!"
* Freddie: "I don't want mac and cheese for lunch. No chiz!"
It's simply a funny phrase that the characters use to express their dislike for cheese or anything they find cheesy.