First, chips are considered "illegal" if they are counterfeit or do not meet state enforced gaming requirements. For example, the colors of casino chips in Atlantic City must be a certain color for each denomination, $1 is white, $5 is red, etc. But, I think that what you were referring to is ... What makes a casino legal or illegal?

A casino is a business that provides gaming. Home (private) games are legal in most states, they are not considered casinos because they are not businesses, just casual games among friends. A casino is seeking to make a profit from gamblers, a private game does not.

A casino is illegal if it is not licensed or if it is located in a state that does not have legal casinos. In the Old West, many states or pre-state territories, did not have any laws making casinos legal or illegal. Poker games in saloons were allowed because there were no gaming regulations. In fact in order for Nevada to become a state in 1864, they had to outlaw gambling. Which, of course, was changed in 1931 in order to bring Nevada out of the depression.