If you don't like using the "chat" feature in Facebook, you can disable it so that people can't contact you via chat.

To disable chat, click on it from any page in Facebook (it's usually in the lower right-hand corner of the screen). Once you click on it, it'll pop up a menu. Select "Options" from the menu. This will pop up yet another menu, select "Go Offline" from that menu and nobody will then be able to contact you via Facebook chat.

When you are offline like this, the offline status will be indicated in the chat (lower right-hand corner) and you can repeat the process to reverse things and re-enable chat.