According to the official site Ledger Live is supported on " 64-bits desktop computer (Windows 8+, macOS 10.8+, Linux), excluding ARM Processors. + Android 7+ or iOS 9+ smartphone." Accordingly to that, I think you'll need to find another way to update the firmware for your Nano S.
There is an option to install Linux on Chromebook, but for most it's not an easy process and something they want to try at all. In your case best option is to find any PC with Windows 10 or Linux, and depending on your current firmware update can be made in just a few minutes.
https://shop.ledger.com/pages/ledger-livehttps://itsfoss.com/install-linux-chromebook/