Chime, a digital bank without a single branch, is picking up steam.

The San Francisco based start-up took about four years to reach its first million customers, crossing that threshold in May 2018 by luring users with the promise of no-fee checking and saving accounts.

This year, Chime added a million customers in roughly the last three months, according to CEO Chris Britt. The bank reached the 4 million mark last month.

"We are by far the fastest growing financial services company in the bank account business," Britt said in a telephone interview. "Our members are coming to us from the big banks. We're a 150 person company, and we're competing with banks with a trillion dollars in assets."

Big banks have talked about the threat from tech-powered upstarts for years, but it's only recently that online banks like Chime have begun to make inroads. When it comes to the core activity of checking and savings accounts, lenders with huge, coast-to-coast branch networks like J.P. Morgan Chase and Bank of America have dominated in the post-financial-crisis era, but Chime appears to have carved out a niche.

The bank focuses on millennials who make $35,000 to $70,000 a year, people who may be frustrated by fees at their brick-and-mortar lenders. That's because this segment leans heavily on using debit cards to pay for everyday expenses while staying within budget, and Chime makes money from the swipe fees paid for by merchants.

"If you make $150,000, you may not love your bank, but you probably don't hate it," Britt said. "I'm not going after that consumer, the credit card rewards seeking person who wants to travel to Europe for free on points."