While gaming tokens do turn up in the collection plates of Las Vegas churches, those churches (Catholic or Protestant) don't all send them out to a "nearby Franciscan monastery" for sorting and redemption by designated "chip monks." Churches generally accumulate gaming tokens until they each individually tab one or more of their workers to take the chips around to casinos and redeem them for cash.
It is true that one church in Las Vegas, the Shrine of the Most Holy Redeemer, once had a Franciscan friar on staff who made the rounds of casino cages and thus, in the fashion of the joke, he was dubbed "the chip monk." Church Employees tasked with handling chip redemptions at various Las Vegas-area churches are sometimes also referred to as "chip monks" in furtherance of the joke, but they are neither real monks nor are they employed by monasteries that sort and redeem the tokens.