>> Gram for gram it's better to eat chicken than cheese for the climate.
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reply>IE a chicken filet is about the carbon impact of 8oz of milk.
They said cheese not milk. Note that it takes more than 1 unit of milk to produce 1 unit of cheese. From this source I found, they estimate ~10 input units of milk per output unit of cheese [1].
Assuming both of these are true, and assuming that the cheese making process produces no carbon, then a chicken filet would have the same carbon impact as .8oz of cheese or roughly a single slice of cheese.
The cheese making process does produce carbon (e.g. heating the milk) but it also produces whey as a valuable byproduct.