Calico cats are female, except for about 1 in 10,000 which are phenotypically male, but can express calico features because they've got XXY chromosomes instead of XY.
In mammals the presence of a Y chromosome will usually result in a phenotypic male. Two X chromosomes are required for calico cats, because orange and black are allelic on the X chromosome. Please note that this is not true for many other species, which orange and black are not linked to sex chromosomes.
It had become somewhat popular to describe a XXY creature as a hermaphrodite, though this isn't exactly correct. Male cats with an extra X are typically fine, though not typical males.
Chickens do not have X and Y chromosomes, but rather W and Z. I think they have Z, some birds rather than having the diminutive Z just simply don't have that chromosome. I think chickens do have a Z.
In birds a WW triggers a male bird, as opposed to XX triggering a female in mammals. WZ or W- for those species without a Z are female.
There can be WWZ birds, just as there can be XXY mammals. I don't know how that would manifest in a chicken. But the likelihood of it manifesting as a true hermaphrodite, with functioning make and female reproductive systems, it's quite small.
In fact, most birds outside of the paleognaths (which is mostly the rattites for farmers and aviculturists) only have one ovary (the left one as I recall).
I don't know if the frequency of chickens with WWZ chromosomes is 1 in 10,000. I think that statistic gets tossed around quite a lot, with little substance to back it. It certainly doesn't require hermaphroditism for a chickens gender to be confusing.
Raise pigeons for a while, or better yet guineas. Then chickens seem simpler in comparison.