Due to some cookie restriction in Lion the latest stable or beta version of Adium cannot connect to Facebook chat.

Luckily they just re-enabled their nightly builds which fix the issue.

Download the latest nightly from: http://nightly.adium.im/

Make sure you get the 1.4.3 nightly currently: http://nightly.adium.im/?repo_branch=adium-1.4-default

As the 1.5 builds are unstable.

Update: Adium have now released a beta fixing this issue: http://beta.adium.im/. Betas are usually more stable than nightlies so use this!