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An earlier review established the LG 27 inch Class Ultra HD IPS 4K 27UD88-W Monitor can charge the HP Chromebook 13 G1 so let's see now how well the monitor works as a screen.  When connecting the LG 27 inch Class Ultra HD IPS 4K 27UD88-W Monitor to the Chromebook 13 G1 directly using a USB Type-C to USB Type-C cable like the one that comes with the LG monitor (make sure you don't use a commonly found USB Type-C cable that is just used for charging and often doesn't support USB 3.1 or DisplayPort 1.2).

Looking at the Chromebook 13 G1's Settings, we can confirm that the LG 27 inch Class Ultra HD IPS 4K 27UD88-W Monitor can display in 4K resolution from the Chromebook.  The Chromebook 13 G1 is using DisplayPort 1.2 to output 4K video over USB Type-C through the DisplayPort Alternate Mode enabled using USB Power Delivery technology.