You can upgrade it as high as High Sierra which is still three OS versions behind the current Big Sur. I don't know if that will satisfy Chrome. Realize in general that unless your computer has been upgraded with more than base RAM and has had a SSD replace the HDD hard drive that this may end up running slowly, particularly with something like Chrome.
Get more information about your computer, choose: (Apple menu) > 'About This Mac' in the upper left corner of any window, then "More Info..." or "System Report". There's more about this in "About System Information [Profiler] on your Mac" - https://support.apple.com/HT203001
Use the computer information, including the model year, and the links below to determine what is possible with your computer.
Click on this link to read how to get different versions of macOS - https://support.apple.com/HT211683
- Make sure you have more RAM (memory) than what is noted as "minimum" for any particular system or your computer may run slowly.
- You may find you need to use Safari to get links for High Sierra and later using the Mac App Store application to open a functioning page.
- Upgrades may take some time (up to an hour or more) to install, with restarts and blank screens.
Before upgrading, back up your data in case something goes wrong. See this support document: Back up your Mac with Time Machine - https://support.apple.com/HT201250 or use a cloning tool.
Check if your old apps will still work with with the OS you want to install - https://roaringapps.com/apps