I'm using Rikaichan for Thunderbird right now, which works great for Japanese but it doesn't do Chinese.

I have Perapera-kun for Firefox which seems to work the same as Rikaichan. It does both Chinese and Japanese.

I've tried installing Perapera-kun in Thunderbird, but no dice. It gives me an incompatibility error.

Are there other options?

Use lingoes. Download it from http://www.lingoes.net/ and then download a chinese dict from here: http://www.lingoes.net/en/dictionary/index.html

Lingoes is free and just works everywhere.. PDFs, Programs etc.