I use Chatterlight, Chatterlighter and My Chatterlight. I don't remember all the features for the three, but this evening it seems none of them can bring up both chat and private messages. I'm sure at least two of the three provide that service, but am pulling out grey hairs to remember all the options. But my instincts say something isn't quite working.
Private messages are provided by default in the chatterbox nodelet, which both chatterlight and chatterlighter use. However, if you have the Messages nodelet disabled, the chatterbox nodelet does not display private messages, so you don't get them listed twice. However, in the case of chatterlight and chatterlighter, this means you have to go to another page to view your private messages.
This is known behavior. My thought on the matter are that (1) chatterlight should be retired and (2) chatterlighter should have a tab for the Messages nodelet if it's enabled.
-om 2011 June 29