There may be a slight performance impact, though its likely to be minimal. 
Google Analytics, in the default configuration, only executes once per page load; Chartbeat, however, will ping the servers every so often to give a heart-beat to the user.
It's not a bad idea to include both; they're really complementary tools, and there is no conflict between them.  
So, besides the widely cached ga.js, which gzipped clocks in at about 12kb, there's not much more overhead, since the 'ping' sent to Google (via __utm.gif) is so lightweight and quick. 
Google Analytics is designed to minimize its performance impact, so you really lose very little by adding it. 
You can minimize its performance impact by:
- Using the asynchronous syntax.
 
- Placing it at the bottom of your pages, just before 
</body> (though even this will provide minimal benefit, since the asynchronous syntax loads Google Analytics in a non-blocking way.) 
EDIT: Also, depending on your needs, you may be able to replace ChartBeat with the new Google Analytics Real Time that was just announced.