In America...
Being a "woman" is about being respected but used to be used to refer, in part, to the fact that you were less than a man.
To be a "Lady" used to be about respect; there were the Lords and Ladies of the lands (there still are, but for us americans they may as well be figments of our imagination). Now, it is an insult and refers, in part, to the fact that you are less than a man.
To be a "chick" is to be fuckable. It's about the body, not the mind. Sometimes used in ways that imply a lack of respect, and sometimes used just to refer to a woman who is youthful, feminine (butch girls don't tend to be reffered to as chicks nearly as often), and sexually attractive. Men can say "chick" but only men who have shown their respect and appreciation for women can do it without it being insulting.
moJoe: Talk to your female friends... In my experience the majority of women under 30 do not find Lady to be a compliment, although I agree it should be. It should also be farly obvious that I am describing the common American, ok the Americanisn't obvious, usage and interpretation, not the actual meanings.