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Hippocrates was fascinated by twins, but the concept and understanding of scientific research was different then from now.
In this work, St. Augustine writes on Cicero's commentary to Hippocrates' observations and speculations regarding one particular pair of brothers, who might have been twins. When the very question is that old, I believe attempts to identify the first such is doomed to be mired in speculation, personal opinion, and the political correctness of assigning it to this culture or that.
For the sake of completeness, here is an 1875 study by Francis Galton.