Sometimes you just want a bit of extra privacy. If you want to appear offline to specific people in Facebook chat for whatever reason, here's how to do it.
Take note that this may change whenever Facebook decides it's time for a site update, which does happen rather frequently.
1. In the left-hand column of your profile, under "Lists", click "More".
2. Click "Create a list".
3. Call the list something easy to remember, like "Invisible", and click "Create list". You will be taken to the list page.
4. Click "Manage list" in the top right-hand corner, then "Add/remove friends". Select the people you want to hide from in the pop-up that appears, and when finished click "Done".
5. Open Facebook chat and click on the gear icon. Select "Limit availability".
6. In the pop-up that appears, set the drop-down menu to "Make me unavailable to". Select your "Invisible" list, and hit "OK".
7. Now everyone added to this group will not see your Facebook chat presence. You can also quickly add people by going to their profile, selecting the "Friends" button in the top right, then clicking on the "Invisible" list.