Depends on your monitor. Do you have 2 HDMI ports? If so, use two different HDMI cables.. one for the PC & one for the Xbox and just switch "sources" on the monitor.
If not, I'm sure your monitor has a standard RGB connection in which case you could pick up the Xbox RGB cable (probably like $25 at Frys Electronics, Best Buy, etc) That way, you could keep the HDMI connection to your PC and use the RGB cable for your Xbox. Again, you'll need to switch "sources" accordingly.
EDIT: Looks like those Xbox RGB cables are hard to come by these days... perhaps a switch box would be more appropriate for you. Here's a link to something that should work: LINKY