The rumors began more than a month ago, on blogs and internet forums: Chase was preparing to unveil a new credit card. Within the thriving online subculture of credit-card churning, obsessed with maximizing reward programs, expectations were high.

The new Chase Sapphire Reserve card, released last week, more than met them. Despite its whopping $450 annual fee, so many people signed up amid the online frenzy that on Wednesday, the bank ran out of the actual cards.

Chase approved "tens of thousands of applications" in the first two days, said spokeswoman Lauren Francis; the majority of the cards are going to millennials. And the bank didn't have enough of the special cards—made with a proprietary mix of embedded metals—to meet the demand, so for the time being, it's sending out regular plastic versions.

"It significantly exceeded our strongest expectations," Francis said.

Chase says it has spent nothing so far on marketing the new Sapphire Reserve card; all the interest in the Sapphire Reserve is coming from word of mouth or the Internet.

Indeed, as credit-card reward programs have grown more generous, online forums and bloggers have become fonts of ingenious ways to exploit them for free travel or cash. To accrue sign-up bonuses, for example, some credit-card churners end up cycling through dozens of credit cards.

Banks, hotels and airlines don't necessarily condone such strategies. But the online buzz among churners and other points-obsessed customers has become a roar that's also reached card offers' broader intended audience: affluent people who travel frequently.

On Reddit's increasingly popular "churning" forum—which has shot up from 42,000 to 53,000 subscribers in just the last four months—a megathread about the Chase Sapphire Reserve card has attracted 10,000 comments.

"I've never seen hype for a card like I saw with this," said Shawn Coomer, a travel blogger in Las Vegas who has been credit-card churning for more than five years.

The card is "magical," said Frank Leppar, a resident of Weirton, West Virginia, who already has his new card. "The sign-up bonus is amazing. It's one of the better, if not the best, card out right now."

What is drawing so many churners, travelers and others to the Sapphire Reserve card are its perks: Cardholders who spend $4,000 in the first three months get a sign-up bonus of 100,000 points, worth $1,500 in travel through Chase's website—and potentially more, some bloggers point out, when transferred to Chase travel partner sites. The card also gives three points for every $1 spent on dining and travel, and its definition of travel—which includes ride-share services like Uber and home-rental services like Airbnb—is broader than other cards'. It also offers a $300 annual credit to reimburse cardholders for travel expenses.

"Once people started finding out about this stuff, it started going crazy" online, Coomer said.

Though both he and his wife applied, he warned against getting too caught up in the enthusiasm online, saying the card might not be right for everyone. Its $450 annual fee raises the stakes for cardholders: That $1,500 in travel rewards isn't the same as $1,500 in cash, and you don't want to pay a hefty annual fee just for travel points you'll never be able to use.

Credit-card companies use generous perks to lure customers who travel frequently and spend freely, but they're wary of churners aiming mainly for free trips and other goodies. The companies are increasingly cracking down on the most hardcore churners, who take out card after card for their sign-up bonuses. Chase's new card application explicitly warns them away: "You will not be approved for this card if you have opened 5 or more bank cards in the last 24 months."

That blocks Dan Miller, a blogger and churner in Cincinnati, from getting one. He's disappointed, but he's philosophical.

"Part of what I enjoy about this is not only traveling," said Miller, who has turned credit-card rewards into free trips to Seattle, Singapore, Dubai and Lake Tahoe.

"This is a game," he said. "The rules change; you have to adapt."

As for the run on the Chase Sapphire Reserve cards? Customers who get the temporary plastic cards can use them as long as they want—but once the metal cards are available again, they can always upgrade.

Having that heavier, fancier card "does make a difference to people," said Leppar, who has one. "The whole purpose of it is to show it's a premier card."

This article was provided by Bloomberg News.