Chime, one of the country's largest so-called challenger banks, might eventually join the ranks of traditional banks.

But the process to get to that decision is long, said Chime co-founder and CEO Chris Britt. Speaking at CB Insights' Future of Fintech conference in New York, Britt said his company might pursue a bank charter at some point. Today, it partners with Wilmington, Del.-based Bancorp Bank.

The debate of whether to become a bank is one that many fintechs are having. Two fintech companies — Varo Bank NA and Robinhood Markets Inc. — have already applied to become full-service banks.

Some fintech companies are rumored to be considering the Office of the Comptroller of the Currency's special-purpose banking charter, though two lawsuits facing the first applicant might be causing potential applicants to delay their submissions. Other digital-focused financial services companies have pursued an industrial loan company charter to secure national regulation.

"We always want to set up a relationship where it's a win-win," Britt said when asked about the economics behind partnering with a bank versus becoming one itself. The San Francisco-based challenger bank, which is known as 1debit Inc. but uses Chime as its marketing name, has attracted a large set of deposits, some of which its partner bank can then monetize in other ways, he added.

Chime launched in 2013 and today announced that it reached 4 million accounts, up from about 1 million a year ago. Speaking onstage at the conference, Britt said he believes the startup could hit 25 million active customers within a few years.

Although neo-banks have struggled to make headway in the U.S., Chime might have found a niche. It focuses on middle-income millennials who want fee-free banking. Chime makes money from swipe fees at the point-of-sale. It also allows its customers to receive their paychecks in advance. Chime has issued over $4 billion in early pay to its customers, Britt said.

In March, Chime posted a $200 million series D round, tripling its post-money valuation to $1.5 billion.

The branchless bank can continue to roll out new products and features today without becoming a full-service bank, Britt said. For now, Chime is focusing on adding those products over time and growing "very aggressively," the chief executive said.