Many people seem to be having this problem. Here's 2 solutions I found.
Fix One
One solution seems to be changing the language settings. If you are set to English (Pirate) or any other variation of your language it seems to cause problems.
Click on Account in the top right corner, then Account Settings. Then on the Language tab. Even if you are set to your native language, change it to something else and then change it back again. For England, set it to English (UK).
Fix Two
Another problem can be when your chat is set to show friends from a certain group.
If you have created a friends list check that chat is not set to just display friends from that list.
In the chat window in feint writing you will see 'other friends' witha small slider on the right. Hover over the slider and if it says 'go online' then give it a click and you list should pop up.
If anyone has found any other solutions, post them below and I'll update the post.