Chase site System requirements: https://www.chase.com/digital/resources/privacy-security/security/system-requirements

Looks like you will have to use a newer computer.

How about trying their app on your phone.

Maybe search for a Linux distribution that supports your hardware.

I am trying to get my Chase online banking and my Firefox is outdated. I have a Max OSx Mountain lion version. How can I get this to work?

Well your Firefox version is indeed outdated. Firefox 78.0 was released three years ago June 30, 2020. The 78.15.0 is just for allowed stability/security fixes since.

Firefox 79.0 and later including current release requires macOS 10.12 (ten.twelve) or later to run.