Timely topic as I too have been thinking about adding a second chick.
Not a second singer, mind you -- just a second chick. Thoughts?
I think that is an entirely different issue. In OP's case, the potential problem (IMO) is that the current singer would perceive the addition of another "chick" singer as a competitor, and might feel like people didn't like her, or that she was in danger of being replaced, etc. As I mentioned before, I would have the exact same concern if the two singers were guys (and especially if the current singer, like OP's, was "unstable" and had a fragile ego). So to me the issue was never "chick-ness" per se. I wouldn't have nearly the same level of concern if OP's band was thinking about adding a second guitarist, for example, who happened to be a woman.