In Google Chrome you cannot set a separate proxy (different from the systemwide proxy) to browse the internet using the basic settings. But you can definitely tweak the settings to set a proxy for Chrome that is not same as the systemwide proxy settings.
explains the thing wonderfully. But it has instructions for both Linux (GNOME) and WIndows. I am just sharing the Linux part here:
Similarly, for Google Chrome in Linux
right click on the Desktop Icon or the Gnome panel Icon and click on properties. In the dialog box that opens, add this line before the %U in the command field.
You can see this screenshot below for a better understanding of the steps as discussed earlier.
Set Separate Proxy in Google Chrome for Linux
You can find more network related command line switches for Google Chrome here