Wells Fargo and Chase each offer online checking accounts, among other banking products. But they also have monthly fees, too. Good news: Well Fargo will eliminate non-sufficient fees funds (NSF) fees in the third quarter of 2022 and give customers early access to eligible direct deposits. Each has online and in-person banking; so, one could be a better fit depending on branch locations in your area. Chase often offers significant new-user sign-on bonuses.