"A male would have XY chromosomes and a female XX. That defines their gender beyond doubt."
Well, it may not be quite so simple. I found a World Health Organization website (http://www.who.int/genomics/gender/en/index1.html#Hermaphroditism) with the following:

“Humans are born with 46 chromosomes in 23 pairs. The X and Y chromosomes determine a person’s sex. Most women are 46XX and most men are 46XY. Research suggests, however, that in a few births per thousand some individuals will be born with a single sex chromosome (45X or 45Y) (sex monosomies) and some with three or more sex chromosomes (47XXX, 47XYY or 47XXY, etc.) (sex polysomies). In addition, some males are born 46XX due to the translocation of a tiny section of the sex determining region of the Y chromosome. Similarly some females are also born 46XY due to mutations in the Y chromosome. Clearly, there are not only females who are XX and males who are XY, but rather, there is a range of chromosome complements, hormone balances, and phenotypic variations that determine sex.”
...
“‘True’ hermaphroditism is a genetic condition in which affected individuals have both mature ovarian and testicular tissue. There are no published population-wide estimates of the frequency of true hermaphrodites. The autosomal inheritance of this condition suggests that genes controlling sexual development and differentiation are not limited to the sex chromosomes.”