I've long considered myself a female chauvinist. That is, I think that women are superior to men (in much the same way that Ayn Rand thought men are superior to women).
My dictionary defines "chauvinism" in part as "unreasoning devotion to one's own race, sex, etc., with contempt for other races, the opposite sex, etc." I'll address the unreasoning part in a minute. First, though, it's obvious that devotion to the opposite sex is not chauvinism on this definition -- although for me to say that I am a female chauvinist has the kind of paradoxical quality that Ayn Rand liked so much. I do consider myself devoted to the opposite sex, so in this sense I am a female chauvinist.
However, I disagree with the implication that such a feeling must be "unreasoning". In fact, it seems perfectly natural for me to admire the strengths and distinctive characteristics that women display, just as it is (at least according to Rand) natural for a woman to admire the strengths and distinctive characteristics that men display. Partly this is a fascination with what Hegelians might call "the other", with beings who are fundamentally the same but so intriguingly different. Partly it is an appreciation of the capabilities that the other has.
I think that this is what Rand was getting at in her attitude towards the other sex. But I think that it is natural for a man to have the same feelings about women that Rand has about men -- admiration, appreciation, the upward glance. Thus I believe that "[Rand's] definition of man includes admiring a woman's femininity", as Christina Mitakis wondered. Of course, the question is: what are the distinguishing characteristics of women in relation to men or of men in relation to women? The traditional definitions -- that women are weak and irrational, incapable of thought, choice, or action -- are wrong. Rand shows this brilliantly with her heroines: they are strong, smart, productive, intelligent, courageous, and so on -- they have "virtu", all of the traditional male excellences. It's obvious that Rand believed that women and men are much more similar than different.
So what are the differences? Besides the obvious differences (anatomy, voice tone, etc.), I think women tend to have better organizational and people skills, tend to be more integrated and more open to emotional experience, tend to communicate better and be more verbally intelligent, and so on. At least, these are things that I admire about women. I'm more hesitant to say how men are different from women, since I think that's something women would notice more, but one example is that men generally have better spatial relations skills than women. Do these things hold for all individuals? No. Are they all that important? I'd say they are interesting and important, but not essential -- it's not literally true that "men are from Mars and women are from Venus", that we can't understand each other, that we're from different species and all that.
As Rand showed with her novels, men and women are more similar than the traditionalists would like to admit -- but we are different, and those differences are causes for fascination, celebration, admiration, and devotion.