Today I learned that Swedish king Gustav III supposedly took two twin brothers that had been convicted for murder and had them drink three pots of coffee and tea respectively per day. He supposedly did this to prove that coffee was bad for you, but ironically he got assassinated before either of the brother died.
However, there seems to be no contemporary records of this twin study so we don't know if it really happened. But that leads me to the question: What was the first documented twin study?
Wikipedia references one in 1905, but that seems to be more about studying twins, than doing the type of twin study where you use twins to look for environmental factors, which is what Gustav III did.
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.