The simple solution to this problem is to create a new List for the friends you want to hide from, and then set that list to offline in Facebook chat. You can start off by clicking on Friends on the left-hand menu.

Then click on the Create a List button, of course…

First, you’ll want to give the list a name—I chose “Hidden Chat” since it seemed logical. Next, add your annoying family members and co-workers to the list, as well as anybody that doesn’t eat delicious Reuben sandwiches.

Now pop up your Facebook Chat screen, and click the little green toggle switch.

At this point you’ll be signed out for those people. Yay!

You can also easily add or remove people from the Hidden Chat list by just clicking the little edit link that launches the List edit screen.

Thanks to Brenna for pointing out this tip.