It's not possible for foreigners to enter Libya from Chad. Even if you could, northern Chad is not an easy area - rebels in the Tibesti, virtually no infrastructure, landmines...
You may be able to get from Chad to Sudan, but I don't think that's possible either at the moment.
The first place you could do a real east-west crossing (apart from going along the coast, which hardly counts as crossing Africa) would be through the CAR, though again this is not exactly a country which sees much tourism (rebels in the north towards the Chadian border).
Are you travelling by motorbike / 4x4? If so are you aware of the paperwork required to get into Egypt? - Carnet de Passages en Douane with a customs indemnity 800% of the value of your vehicle. Even with this, you still need to leave deposits at the border.
You're best bet is probably across the Sahara and down the west coast route to South Africa. I'll be doing this in October, crossing Algeria into Niger, so let me know if you're going at the same sort of time.
I hope this isn't putting you off, but it's not as easy as the map makes it look! Otherwise, we'd all be taking holidays in the Tibesti.
Log onto the Sahara travel page for more info.
[This message has been edited by danielsprague (edited 26 March 2006).]