Great question - I'm glad you included what you are taking the Paxil for. So in answer to your direct question - no, there is no interaction between Paxil and Chantix. They may be taken together (you should mention it to your prescribing physician though).
That said, there are several side effect to Chantix as well as quitting smoking. Chantix can cause very vivid dreams that can be unsettling to some people. Also, there have been some reports of people getting some depression with Chantix.
Finally, (as I'm sure you're aware), quitting smoking can cause irritability and anxiety in most people. So, you might get a spike in your anxiety due to that.
I hope this answers your question - please let me know if there is anything else I can help you with!