I think AdSense and Chitika are OK to use together. Chitika is not contextual from what I understand, therefore they can be used together. I don't use Chitika, but that is my understanding. Don't take my word for it though, probably.
Actually yes, it is ok. There are lots of websites that use both these networks. As mentioned by mmm555, Chitika is non-contextual and also doesn't "look like Adsense" and thus it can be used in unison. You can find this information on the Chitika site: http://chitika.com/publishers/
I don't think you'll get any problems using both. As far as I remember, there's no prohibition in the Adsense rules that don't let using another PPC systems with Adsense.